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Journal articles on the topic 'Impulsive conditions'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

ZENG, GUANG-ZHAO, and LAN-SUN CHEN. "COMPLEXITY AND ASYMPTOTICAL BEHAVIOR OF A SIRS EPIDEMIC MODEL WITH PROPORTIONAL IMPULSIVE VACCINATION." Advances in Complex Systems 08, no. 04 (2005): 419–31. http://dx.doi.org/10.1142/s0219525905000580.

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This paper considers an SIRS epidemic model with proportional impulsive vaccination, which may inherently oscillate. We study the ratio-dependent impulsive control and obtain the conditions about the basic reproductive number for which the epidemic-elimination solution is globally asymptotic. On the other hand, if the epidemic turns out to be endemic, we study numerically the influences of impulsive vaccination on the periodic oscillation of a system without impulsion and find sophisticated phenomena such as chaos in this case.

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2

Uğurlu, Ekin, and Elgiz Bairamov. "Dissipative operators with impulsive conditions." Journal of Mathematical Chemistry 51, no. 6 (2013): 1670–80. http://dx.doi.org/10.1007/s10910-013-0172-5.

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3

Allahverdiev, Bilender P., Hüseyin Tuna, and Hamlet A. Isayev. "Fractional Dirac system with impulsive conditions." Chaos, Solitons & Fractals 176 (November 2023): 114099. http://dx.doi.org/10.1016/j.chaos.2023.114099.

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4

Li, Biwen, and Qiaoping Huang. "Synchronization of time-delay systems with impulsive delay via an average impulsive estimation approach." Mathematical Biosciences and Engineering 21, no. 3 (2024): 4501–20. http://dx.doi.org/10.3934/mbe.2024199.

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<abstract><p>We investigated synchronization of dynamic systems with mixed delays and delayed impulses. Using impulsive control method and the average impulsive interval approach, several Lyapunov sufficient conditions were given for ensuring synchronization in terms of impulsive perturbation and impulsive control, respectively. The derived conditions indicated that delays in continuous dynamical systems were flexible under impulsive perturbation and were not strictly dependent on the size of impulsive delays, and they may have a potential impact on synchronization of the considere

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5

Mahmudov, Nazim I., and Amal M. Almatarneh. "Stability of Ulam–Hyers and Existence of Solutions for Impulsive Time-Delay Semi-Linear Systems with Non-Permutable Matrices." Mathematics 8, no. 9 (2020): 1493. http://dx.doi.org/10.3390/math8091493.

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In this paper, the stability of Ulam–Hyers and existence of solutions for semi-linear time-delay systems with linear impulsive conditions are studied. The linear parts of the impulsive systems are defined by non-permutable matrices. To obtain solution for linear impulsive delay systems with non-permutable matrices in explicit form, a new concept of impulsive delayed matrix exponential is introduced. Using the representation formula and norm estimation of the impulsive delayed matrix exponential, sufficient conditions for stability of Ulam–Hyers and existence of solutions are obtained.

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6

Babiarz, Artur, Jerzy Klamka, and Michał Niezabitowski. "Schauder’s fixed-point theorem in approximate controllability problems." International Journal of Applied Mathematics and Computer Science 26, no. 2 (2016): 263–75. http://dx.doi.org/10.1515/amcs-2016-0018.

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AbstractThe main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with

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7

Mahmudov, Nazim I., and Gülbahar Akgün. "A Study on Existence and Controllability of Conformable Impulsive Equations." Axioms 12, no. 8 (2023): 787. http://dx.doi.org/10.3390/axioms12080787.

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We study the existence/uniqueness of conformable fractional type impulsive nonlinear systems as well as the controllability of linear/semilinear conformable fractional type impulsive controlled systems. Using the conformable fractional derivative approach, we introduce the conformable controllability operator and the conformable controllability Gramian matrix in order to obtain the necessary and sufficient conditions for the complete controllability of linear impulsive conformable systems. We present a set of sufficient conditions for the controllability of the conformable semilinear impulsive

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8

Liu, Xinzhi, Xuemin Shen, and Yi Zhang. "A comparison principle and stability for large-scale impulsive delay differential systems." ANZIAM Journal 47, no. 2 (2005): 203–35. http://dx.doi.org/10.1017/s1446181100009998.

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AbstractThis paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.

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9

Chai, Xiuli, Zhihua Gan, and Chunxiao Shi. "Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/751616.

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The impulsive synchronization and adaptive-impulsive synchronization of a novel financial hyperchaotic system are investigated. Based on comparing principle for impulsive functional differential equations, several sufficient conditions for impulsive synchronization are derived, and the upper bounds of impulsive interval for stable synchronization are estimated. Furthermore, a nonlinear adaptive-impulsive control scheme is designed to synchronize the financial system using invariant principle of impulsive dynamical systems. Moreover, corresponding numerical simulations are presented to illustra

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10

Silva, Lucas Emmanuel Nascimento, Manoel Bastos Gomes Neto, Patrick Wendell Barbosa Lessa, and Rebeca Da Rocha Grangeiro. "Consumer’s Choices in Critical Conditions: How impulsive buying tendency makes consumers seek foreign products." CBR - Consumer Behavior Review 5, no. 2 (2021): 158. http://dx.doi.org/10.51359/2526-7884.2021.248823.

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The COVID-19 pandemic brought the attention of researchers to impulsive buying behaviors and the purchasing of local products, as they are fundamental for the economic recovery of the countries. Therefore, the purpose of this paper is to identify how the consumer’s impulsive buying tendencies influence their choices for foreign products. We applied the Impulsive Buying Tendency Scale and the X-Scale of Xenocentrism to 300 young and adults. To analyze the data, we conducted a PLS-SEM analysis to test five hypotheses. Our results from the path analysis indicate that the affective aspects of impu

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11

Fang, Yang, Kang Yan, and Kelin Li. "Synchronization of Chaotic Delayed Neural Networks via Impulsive Control." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/305264.

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This paper is concerned with the impulsive synchronization problem of chaotic delayed neural networks. By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. Based on these new sufficient conditions, an impulsive controller is designed. Moreover, the stable impulsive interval of synchronized neural networks is objectively estimated by combining the MATLAB LMI toolbox and one of the two given equations. Tw

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12

Kim, Young-Taek, and Jong-In Lee. "Wave Overtopping Formula for Impulsive and Non-Impulsive Wave Conditions against Vertical Wall." Journal of Korean Society of Coastal and Ocean Engineers 27, no. 3 (2015): 175–81. http://dx.doi.org/10.9765/kscoe.2015.27.3.175.

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13

Zhao, Wanshun, Kelin Li, and Yanchao Shi. "Exponential synchronization of neural networks with mixed delays under impulsive control." Electronic Research Archive 32, no. 9 (2024): 5287–305. http://dx.doi.org/10.3934/era.2024244.

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<p>In this paper, the exponential synchronization problem of a class of neural networks with mixed delays under impulsive control is studied. Combining the impulsive comparison principle and the concept of an average impulsive interval, two impulsive differential inequalities with mixed delays are discussed, and the sufficient conditions for the existence of exponential decay are obtained. Based on two different impulsive control strategies, and then by means of the Lyapunov function, the inequality technique, and these two new inequalities, a set of sufficient conditions are derived to

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14

Ji, Yanjie, and Zhaoyan Wu. "Outer Synchronization of Complex-Variable Networks with Complex Coupling via Impulsive Pinning Control." Mathematics 9, no. 17 (2021): 2110. http://dx.doi.org/10.3390/math9172110.

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In this paper, outer synchronization of complex-variable networks with complex coupling is considered. Sufficient conditions for achieving outer synchronization using static impulsive pinning controllers are first derived according to the Lyapunov function method and stability theory of impulsive differential equations. From these conditions, the necessary impulsive gains and intervals for given networks can be easily calculated. Further, an adaptive strategy is introduced to design universal controllers and avoid repeated calculations for different networks. Notably, the estimation algorithms

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15

You, Zhongli, JinRong Wang, and D. O’Regan. "Asymptotic stability of solutions of impulsive multi-delay differential equations." Transactions of the Institute of Measurement and Control 40, no. 15 (2018): 4143–52. http://dx.doi.org/10.1177/0142331217742966.

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In this paper, we consider the asymptotic stability of solutions to impulsive multi-delayed differential equations with linear parts defined by pairwise permutable matrices. First, we introduce the concept for an impulsive multi-delayed Cauchy matrix and then use it to obtain the representation of solutions to linear impulsive Cauchy problems via the variation of constants principle. Next, we give a norm estimate of the impulsive multi-delayed Cauchy matrix and establish sufficient conditions to guarantee that the trivial solutions are asymptotically stable when the nonlinear terms satisfy app

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16

Akça, Haydar, Abdelkader Boucherif, and Valéry Covachev. "Impulsive functional-differential equations with nonlocal conditions." International Journal of Mathematics and Mathematical Sciences 29, no. 5 (2002): 251–56. http://dx.doi.org/10.1155/s0161171202012887.

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The existence, uniqueness, and continuous dependence of a mild solution of an impulsive functional-differential evolution nonlocal Cauchy problem in general Banach spaces are studied. Methods of fixed point theorems, of aC0semigroup of operators and the Banach contraction theorem are applied.

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17

Santra, Shyam Sundar, Hammad Alotaibi, Samad Noeiaghdam, and Denis Sidorov. "On Nonlinear Forced Impulsive Differential Equations under Canonical and Non-Canonical Conditions." Symmetry 13, no. 11 (2021): 2066. http://dx.doi.org/10.3390/sym13112066.

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This study is connected with the nonoscillatory and oscillatory behaviour to the solutions of nonlinear neutral impulsive systems with forcing term which is studied for various ranges of of the neutral coefficient. Furthermore, sufficient conditions are obtained for the existence of positive bounded solutions of the impulsive system. The mentioned example shows the feasibility and efficiency of the main results.

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18

Wang, Rong-Nian, and Jun Xia. "Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions." Advances in Difference Equations 2011, no. 1 (2011): 634701. http://dx.doi.org/10.1155/2011/634701.

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19

Silva, G. N., and R. B. Vinter. "Necessary Conditions for Optimal Impulsive Control Problems." SIAM Journal on Control and Optimization 35, no. 6 (1997): 1829–46. http://dx.doi.org/10.1137/s0363012995281857.

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20

Arutyunov, A., V. Dykhta, D. Karamzin, and F. Pereira. "Necessary optimality conditions for impulsive control problems *." IFAC Proceedings Volumes 37, no. 17 (2004): 2–12. http://dx.doi.org/10.1016/s1474-6670(17)30792-9.

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21

Bortnyk, Nadia, Iryna Zharovs'ka, and Maryana Tsvok. "Impulsive causes of migration in modern conditions." Visnik Nacional’nogo universitetu «Lvivska politehnika». Seria: Uridicni nauki 2017, no. 884 (2017): 80–87. http://dx.doi.org/10.23939/law2017.884.080.

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22

Moayery, Meysam, Lorea Narvaiza Cantín, and Juan José Gibaja Martíns. "Reflective and Impulsive Predictors of Unhealthy Snack Impulse Buying." Review of Marketing Science 16, no. 1 (2019): 49–84. http://dx.doi.org/10.1515/roms-2018-0038.

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Abstract While impulse buying has been conceptualized as a product of impulses, this study proposes that both reflective and impulsive determinants can outline impulse buying. Following a dual-system model that distinguishes between a reflective and an impulsive system, we hypothesized that unhealthy snack impulse buying can be differentially influenced by either impulsive system or reflective system as a function of self-regulatory resources. Participants in the experiment were randomly assigned to one of the conditions of the two-group design (self-regulatory resources depletion vs. control

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23

Singla, Jahnavi, and Amandeep Singh. "Impulsive Attitude and Cryptocurrency investment Behaviour: Investigating the Interplay with trust, risk, and facilitating conditions." International Journal of Information Technology and Management 20, no. 1 (2025): 92–109. https://doi.org/10.29070/fxfr7s12.

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Cryptocurrency has emerged as a disruptive force in finance, attracting considerable attention from investors and scholars alike. This research study investigates cryptocurrency investing, aiming to provide a comprehensive analysis of the many aspects influencing investment behavior in this domain. The present research examined the influence of perceived trust, risk tolerance, and enabling factors on investors' impulsive attitudes. The study examined the influence of impulsive attitudes, perceived behavioral control, and subjective norms on bitcoin investing behavior. Data was collected from 3

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24

Algolam, Mohamed S., Sadam Hussain, Bakri A. I. Younis, et al. "Stability and Controllability Analysis of Stochastic Fractional Differential Equations Under Integral Boundary Conditions Driven by Rosenblatt Process with Impulses." Fractal and Fractional 9, no. 3 (2025): 146. https://doi.org/10.3390/fractalfract9030146.

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Differential equations are frequently used to mathematically describe many problems in real life, but they are always subject to intrinsic phenomena that are neglected and could influence how the model behaves. In some cases like ecosystems, electrical circuits, or even economic models, the model may suddenly change due to outside influences. Occasionally, such changes start off impulsively and continue to exist for specific amounts of time. Non-instantaneous impulses are used in the creation of the models for this kind of scenario. In this paper, a new class of non-instantaneous impulsive ψ-C

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25

Minhós, Feliz, and Rui Carapinha. "Functional Coupled Systems with Generalized Impulsive Conditions and Application to a SIRS-Type Model." Journal of Function Spaces 2021 (August 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/3758274.

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In this paper, we consider a first-order coupled impulsive system of equations with functional boundary conditions, subject to the generalized impulsive effects. It is pointed out that this problem generalizes the classical boundary assumptions, allowing two-point or multipoint conditions, nonlocal and integrodifferential ones, or global arguments, as maxima or minima, among others. Our method is based on lower and upper solution technique together with the fixed point theory. The main theorem is applied to a SIRS model where to the best of our knowledge, for the first time, it includes impuls

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26

Wang, JinRong, Ahmed Gamal Ibrahim, and Donal O’Regan. "Hilfer-type fractional differential switched inclusions with noninstantaneous impulsive and nonlocal conditions." Nonlinear Analysis: Modelling and Control 23, no. 6 (2018): 921–41. http://dx.doi.org/10.15388/na.2018.6.7.

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In this paper, we study a new class of nonlocal problems for noninstantaneous impulsive Hilfer-type fractional differential switched inclusions in Banach spaces. First, we introduce a mild solution formula for this noninstantaneous impulsive inclusion problem. Second, we show the existence of mild solutions using the Hausdorff measure of noncompactness on the space of piecewise weighted continuous functions. Finally, an example is provided to illustrate the theory.

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27

HERNÁNDEZ, EDUARDO, and DONAL O’REGAN. "EXISTENCE RESULTS FOR A CLASS OF ABSTRACT IMPULSIVE DIFFERENTIAL EQUATIONS." Bulletin of the Australian Mathematical Society 87, no. 3 (2013): 366–85. http://dx.doi.org/10.1017/s0004972713000154.

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AbstractWe study the existence of solutions for a class of abstract impulsive differential equations. Our technical framework allows us to study partial differential equations with impulsive conditions involving partial derivatives and nonlinear expressions of the solution. Some applications to impulsive partial differential equations are presented.

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28

Santra, Shyam Sundar, Khaled Mohamed Khedher, Kamsing Nonlaopon, and Hijaz Ahmad. "New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions." Symmetry 13, no. 6 (2021): 934. http://dx.doi.org/10.3390/sym13060934.

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The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges t

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29

Haddad, Wassim M., VijaySekhar Chellaboina, Qing Hui, and Sergey Nersesov. "Vector dissipativity theory for large-scale impulsive dynamical systems." Mathematical Problems in Engineering 2004, no. 3 (2004): 225–62. http://dx.doi.org/10.1155/s1024123x04310021.

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Modern complex large-scale impulsive systems involve multiple modes of operation placing stringent demands on controller analysis of increasing complexity. In analyzing these large-scale systems, it is often desirable to treat the overall impulsive system as a collection of interconnected impulsive subsystems. Solution properties of the large-scale impulsive system are then deduced from the solution properties of the individual impulsive subsystems and the nature of the impulsive system interconnections. In this paper, we develop vector dissipativity theory for large-scale impulsive dynamical

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Wulandari, Anisya, Salsabila Zahrah, Nadiya Qothrunnada, and Lathipah Hasanah. "ANALISIS FAKTOR LINGKUNGAN TEMPAT TINGGAL TERHADAP PERILAKU IMPULSIF ANAK ADHD." Jurnal Peneliti dan Praktisi PAUD 3, no. 2 (2024): 24–32. https://doi.org/10.21009/jp2paud.032.04.

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This study aims to determine the causes of children behaving impulsively, namely the condition of children who cannot control their behavior, so they need special attention. This type of research is a case study with a qualitative approach. This study was conducted in Cakung District to further review the factors of the residential environment on the impulsive behavior of ADHD children. Attention-Deficit/Hyperactivity Disorder (ADHD) is one type of child with special needs. Children with special needs (ABK) are children who have abnormal conditions and differences from the average normal child

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Quan, Qi, Xiangjun Dai, and Jianjun Jiao. "Dynamics of a Predator–Prey Model with Impulsive Diffusion and Transient/Nontransient Impulsive Harvesting." Mathematics 11, no. 14 (2023): 3254. http://dx.doi.org/10.3390/math11143254.

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Harvesting is one of the ways for humans to realize economic interests, while unrestricted harvesting will lead to the extinction of populations. This paper proposes a predator–prey model with impulsive diffusion and transient/nontransient impulsive harvesting. In this model, we consider both impulsive harvesting and impulsive diffusion; additionally, predator and prey are harvested simultaneously. First, we obtain the subsystems of the system in prey extinction and predator extinction. We obtain the fixed points of the subsystems by the stroboscopic map theories of impulsive differential equa

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32

Hartung, Ferenc, Manuel Pinto, and Ricardo Torres. "Uniform approximation of a class of impulsive delayed Hopfield neural networks on the half-line." Electronic Journal of Qualitative Theory of Differential Equations, no. 63 (2024): 1–29. http://dx.doi.org/10.14232/ejqtde.2024.1.63.

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In this work, we investigate a uniform approximation of a nonautonomous delayed CNN-Hopfield-type impulsive system with an associated impulsive differential system where a partial discretization is introduced with the help of piecewise constant arguments. Sufficient conditions are formulated, which imply that the error estimate decays exponentially with time on the half-line [ 0 , ∞ ) . A critical step for the proof of this estimate is to show that, under the assumed conditions, the solutions of the Hopfield impulsive system are exponentially bounded and exponentially stable. A bounded coeffic

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Chen, Xingru, Haibo Gu, and Yu Sun. "Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions." Journal of Function Spaces 2020 (December 1, 2020): 1–9. http://dx.doi.org/10.1155/2020/3142801.

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In this paper, we investigate a class of impulsive Katugampola fractional differential equations with nonlocal conditions in a Banach space. First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. Secondly, we derive the sufficient conditions for optimal controls by building approximating minimizing sequences of functions twice.

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Xie, Xiang, Honglei Xu, and Rong Zhang. "Exponential Stabilization of Impulsive Switched Systems with Time Delays Using Guaranteed Cost Control." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/126836.

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This paper investigates the stabilization problem for impulsive switched systems with time delays. First, exponential stability criteria of the delayed impulsive switched systems are established by use of the Lyapunov-Krasovskii functional method. Based on these results, sufficient conditions for the existence of a guaranteed cost control are also given. Subject to these sufficient conditions, the closed-loop impulsive switched system under the guaranteed cost control law will be exponentially stable with a guaranteed cost value.

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35

Mardanov, Mısır J., Yagub A. Sharifov, and Kamala E. Ismayilova. "Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions." e-Journal of Analysis and Applied Mathematics 1, no. 1 (2018): 21–36. http://dx.doi.org/10.2478/ejaam-2018-0003.

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AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schae

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Chalishajar, Dlmplekumar N., Kulandhivel Karthikeyan, and Dhachinamoorthi Tamizharasan. "Controllability of Nonlocal Impulsive Functional Differential Equations with Measure of Noncompactness in Banach Spaces." Tatra Mountains Mathematical Publications 79, no. 2 (2021): 59–80. http://dx.doi.org/10.2478/tmmp-2021-0020.

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Abstract This paper is concerned with the controllability of impulsive differential equations with nonlocal conditions. First, we establish a property of measure of noncompactness in the space of piecewise continuous functions. Then, by using this property and Darbo-Sadovskii’s Fixed Point Theorem, we get the controllability of nonlocal impulsive differential equations under compactness conditions, Lipschitz conditions and mixed-type conditions, respectively.

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Stamova, I. M. "BOUNDEDNESS OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE IMPULSIVE PERTURBATIONS." Bulletin of the Australian Mathematical Society 77, no. 2 (2008): 331–45. http://dx.doi.org/10.1017/s0004972708000439.

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AbstractIn the present paper an initial value problem for impulsive functional differential equations with variable impulsive perturbations is considered. By means of piecewise continuous functions coupled with the Razumikhin technique, sufficient conditions for boundedness of solutions of such equations are found.

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Assanova, Anar, and Altynai Molybaikyzy. "Solution to the periodic problem for the impulsive hyperbolic equation with discrete memory." Kazakh Mathematical Journal 25, no. 1 (2025): 16–27. https://doi.org/10.70474/kmj-25-1-02.

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In this article, we consider the periodic problem for the impulsive hyperbolic equation with discrete memory. Impulsive hyperbolic equations with discrete memory arise as a mathematical model for describing physical processes in the neural networks, discontinuous dynamical systems, hybrid systems, and etc. Questions of the existence and construction of solutions to periodic problems for impulsive hyperbolic equations with discrete memory remain important issues in the theory of discontinuous partial differential equations. To find the solvability conditions of this problem we apply Dzhumabaev’

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C, Ravichandran, and Valliammal N. "NONLOCAL CONTROLLABILITY OF IMPULSIVE FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES." Kongunadu Research Journal 3, no. 2 (2016): 1–6. http://dx.doi.org/10.26524/krj138.

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The paper is concerned with the controllability of impulsive functional integrodifferential equations with nonlocal conditions. Using the measure of noncompactness and Monch fixed point theorem, we establish some sufficient conditions for controllability and also our theorems extend some analogous results of (impulsive) control systems.

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Li, Huijuan, and Qingxia Ma. "Finite-Time Lyapunov Functions and Impulsive Control Design." Complexity 2020 (October 27, 2020): 1–9. http://dx.doi.org/10.1155/2020/5179752.

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In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

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Liu, Yong Jun, and Peng Qin. "Analysis of Stability of Hopfield Neural Networks and Design of Impulsive Controller." Advanced Materials Research 898 (February 2014): 720–24. http://dx.doi.org/10.4028/www.scientific.net/amr.898.720.

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Based on the proper Lyapunov functions and the Riccati liner inequality, the Robust H-stability of Hopfield neural networks with impulsive effects is studied and some sufficient conditions for robust H-stability are established, the impulsive stabilization criteria can be verified by the impulsive controller, simulation validate the main results.

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You, Zhongli, JinRong Wang, Yong Zhou, and Michal Fečkan. "Representation of Solutions and Finite Time Stability for Delay Differential Systems with Impulsive Effects." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 2 (2019): 205–21. http://dx.doi.org/10.1515/ijnsns-2018-0137.

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AbstractIn this paper, we study finite time stability for linear and nonlinear delay systems with linear impulsive conditions and linear parts defined by permutable matrices. We introduce a new concept of impulsive delayed matrix function and apply the variation of constants method to seek a representation of solution of linear impulsive delay systems, which can be well used to deal with finite time stability. We establish sufficient conditions for the finite time stability results by using the properties of impulsive delayed matrix exponential and Gronwall’s integral inequalities. Finally, we

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43

Fu, Xi, and Xiaoyou Liu. "Existence Results for Fractional Differential Equations with Separated Boundary Conditions and Fractional Impulsive Conditions." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/785078.

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This paper is concerned with the fractional separated boundary value problem of fractional differential equations with fractional impulsive conditions. By means of the Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

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Farkhod, Asrorov, Sobchuk Valentyn, and Kurylko Оlexandr. "FINDING OF BOUNDED SOLUTIONS TO LINEAR IMPULSIVE SYSTEMS." Eastern-European Journal of Enterprise Technologies 6, no. 4 (102) (2019): 14–20. https://doi.org/10.15587/1729-4061.2019.178635.

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The problem of the existence of bounded on the entire real axis solutions to linear nonhomogeneous systems of differential equations undergoing impulsive perturbations at the fixed moments of time is investigated. Sufficient conditions for the hyperbolicity of solutions to the homogeneous multidimensional impulsive system are obtained. The derived conditions are applied to the study of the bounded solutions to the nonhomogeneous impulsive system. Sufficient conditions for the existence of a unique bounded solution to the nonhomogeneous system in the case of weak regularity of the corresponding

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WU, RANCHAO, and DONGXU CAO. "FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA NONLINEAR ADAPTIVE–IMPULSIVE CONTROL." International Journal of Modern Physics C 22, no. 11 (2011): 1281–91. http://dx.doi.org/10.1142/s0129183111016890.

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In this paper, function projective synchronization of chaotic systems is investigated through nonlinear adaptive–impulsive control. To achieve synchronization, suitable nonlinear continuous and impulsive controllers are designed, according to invariant principle of impulsive dynamical systems. Sufficient conditions are given to ensure the synchronization. Numerical simulation results show the effectiveness of the proposed scheme.

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Li, Yaohong, Yongqing Wang, Donal O’Regan, and Jiafa Xu. "Existence of Solutions for a Periodic Boundary ValueProblem with Impulse and Fractional Derivative Dependence." Journal of Mathematics 2020 (December 28, 2020): 1–16. http://dx.doi.org/10.1155/2020/6625056.

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In this paper, we present some theorems on impulsive periodic boundary value problems with fractional derivative dependence. In particular, we discuss the existence of solutions of a class of fractional-order impulsive periodic boundary values with nonlinear terms and impulsive terms satisfying certain growth conditions. Three examples are provided to illustrate our results.

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Wei, Chunjin, and Lansun Chen. "Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/607105.

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A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results

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Ergören, Hilmi. "Impulsive fractional differential inclusions with flux boundary conditions." Filomat 31, no. 4 (2017): 953–61. http://dx.doi.org/10.2298/fil1704953e.

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In this work we investigate some existence results for solutions of a boundary value problem for impulsive fractional differential inclusions supplemented with fractional flux boundary conditions by applying Bohnenblust-Karlin?s fixed point theorem for multivalued maps.

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Qin, Haiyong, Zhenyun Gu, Youliang Fu, and Tongxing Li. "Existence of Mild Solutions and Controllability of Fractional Impulsive Integrodifferential Systems with Nonlocal Conditions." Journal of Function Spaces 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6979571.

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This paper is concerned with the existence results of nonlocal problems for a class of fractional impulsive integrodifferential equations in Banach spaces. We define a piecewise continuous control function to obtain the results on controllability of the corresponding fractional impulsive integrodifferential control systems. The results are obtained by means of fixed point methods. An example to illustrate the applications of our main results is given.

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Li, Biwen, and Qiaoping Huang. "Synchronization issue of uncertain time-delay systems based on flexible impulsive control." AIMS Mathematics 9, no. 10 (2024): 26538–56. http://dx.doi.org/10.3934/math.20241291.

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<p>This paper discusses a synchronization issue of uncertain time-delay systems via flexible delayed impulsive control. A new Razumikhin-type inequality is presented, considering adjustable parameters the $ \varpi(t) $, which relies on flexible impulsive gain. For the uncertain time-delay systems where delay magnitude is not constrained to impulsive intervals, sufficient conditions for global exponential synchronization (GES) are established. Furthermore, based on Lyapunov theory, a new differential inequality and linear matrix inequality design, and a flexible impulsive control method i

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