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Journal articles on the topic 'Almost periodic solution'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Wu, Huaiqin, and Luying Zhang. "Almost Periodic Solution for Memristive Neural Networks with Time-Varying Delays." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/716172.

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This paper is concerned with the dynamical stability analysis for almost periodic solution of memristive neural networks with time-varying delays. Under the framework of Filippov solutions, by applying the inequality analysis techniques, the existence and asymptotically almost periodic behavior of solutions are discussed. Based on the differential inclusions theory and Lyapunov functional approach, the stability issues of almost periodic solution are investigated, and a sufficient condition for the existence, uniqueness, and global exponential stability of the almost periodic solution is estab

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2

Liang, Jiarong, Yongqing Liu, and Cunchen Gao. "Almost periodic solution to singular systems." Chinese Science Bulletin 43, no. 8 (1998): 698–700. http://dx.doi.org/10.1007/bf02883581.

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3

ZHUO, XIANGLAI. "THE STABILITY AND ALMOST PERIODIC SOLUTION FOR GENERALIZED LOGISTIC ALMOST PERIODIC SYSTEM WITH DELAYS." International Journal of Biomathematics 04, no. 03 (2011): 313–28. http://dx.doi.org/10.1142/s1793524511001210.

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The stability and almost periodic solution for generalized logistic almost periodic system with infinite and discrete delays is considered. Some sufficient conditions for the boundedness of the system are obtained to guarantee that the system is globally asymptotically stable. We also show that the almost periodic system has a unique globally asymptotically stable strictly positive almost periodic solution by using the almost periodic functional Hull theory and new computational techniques. Furthermore, some recent results are improved, and an open question is answered.

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4

Chen, Yong Qing, and Hong Xu Li. "ASYMPTOTICALLY -ALMOST PERIODIC SOLUTIONS TO DIFFERENTIAL EQUATIONS IN BANACH SPACES." Far East Journal of Mathematical Sciences (FJMS) 141, no. 4 (2024): 299–316. http://dx.doi.org/10.17654/0972087124018.

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In this paper, we establish the existence and uniqueness result of asymptotically $(\omega, c)$-almost periodic mild solutions to semilinear differential equations in a Banach space. For this purpose, we first give some properties of $(\omega, c)$-almost periodic functions and asymptotically $(\omega, c)$-almost periodic functions, including the composition theorems. Then we obtain the existence and uniqueness result of $(\omega, c)$-almost periodic mild solution to the semilinear differential equation, and the existence and uniqueness theorems for $(\omega, c)$-almost periodic and asymptotica

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5

Lassoued, Dhaou, and Michal Fečkan. "Boundedness and almost periodicity of solutions of linear differential systems." Mathematica Slovaca 72, no. 5 (2022): 1203–14. http://dx.doi.org/10.1515/ms-2022-0082.

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Abstract In this paper, we study the following linear differential system (1) x ′ ( t ) = A ( t ) x ( t ) , x ( t ) ∈ ℝ n , t ∈ ℝ , $${{x}^{\prime }}(t)=A(t)x(t),\,\,\,\,x(t)\in {{\mathbb{R}}^{n}},\quad t\in \mathbb{R},$$ where t ↦ A(t) is a matrix valued almost periodic function. We prove that if all the solutions of the above system are almost periodic, there exists an almost periodic function b : R → R n such that the following differential equation (2) x ′ ( t ) = A ( t ) x ( t ) + b ( t ) , x ( t ) ∈ ℝ n , t ∈ ℝ $${{x}^{\prime }}(t)=A(t)x(t)+b(t),\,\,\,\,x(t)\in {{\mathbb{R}}^{n}},\quad t

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6

Shao, Qi, and Yongkun Li. "Almost periodic solutions for Clifford-valued stochastic shunting inhibitory cellular neural networks with mixed delays." AIMS Mathematics 9, no. 5 (2024): 13439–61. http://dx.doi.org/10.3934/math.2024655.

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<abstract><p>We adopted a non decomposition method to study the existence and stability of Stepanov almost periodic solutions in the distribution sense of stochastic shunting inhibitory cellular neural networks (SICNNs) with mixed time delays. Due to the lack of linear structure in the set composed of Stepanov almost periodic stochastic processes in the distribution sense. Due to the lack of linear structure in the set composed of distributed Stepanov periodic stochastic processes, it poses difficulties for the existence of Stepanov almost periodic solutions in the distribution sen

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7

Ma, Rui, and Mengmeng Li. "Almost Periodic Solution for Forced Perturbed Non-Instantaneous Impulsive Model." Axioms 11, no. 10 (2022): 496. http://dx.doi.org/10.3390/axioms11100496.

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In this paper we investigate a forced perturbed non-instantaneous impulsive model. Firstly, we prove the existence and uniqueness of an almost periodic solution for the model considered by the Banach contraction principle. Secondly, we prove that all solutions converge exponentially to the almost periodic solution. In other words, the solution of the model considered is exponentially stable. Finally, we provide some simulations to show the effectiveness of the theoretical results.

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8

Chen, Ye-Jun, and Hui-Sheng Ding. "Pseudo almost periodicity for stochastic differential equations in infinite dimensions." Electronic Journal of Differential Equations 2023, no. 01-37 (2023): 34. http://dx.doi.org/10.58997/ejde.2023.34.

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In this article, we introduce the concept of p-mean θ-pseudo almost periodic stochastic processes, which is slightly weaker than p-mean pseudo almost periodic stochastic processes. Using the operator semigroup theory and stochastic analysis theory, we obtain the existence and uniqueness of square-mean θ-pseudo almost periodic mild solutions for a semilinear stochastic differential equation in infinite dimensions. Moreover, we prove that the obtained solution is also pseudo almost periodic in path distribution. It is noteworthy that the ergodic part of the obtained solution is not only ergodic

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9

Xue, Yalong, Xiangdong Xie, Fengde Chen, and Rongyu Han. "Almost Periodic Solution of a Discrete Commensalism System." Discrete Dynamics in Nature and Society 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/295483.

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A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.

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10

Meng, Junxia. "Global Exponential Stability of Positive Pseudo-Almost-Periodic Solutions for a Model of Hematopoiesis." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/463076.

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This paper presents a new generalized model of hematopoiesis with multiple time-varying delays. The main purpose of this paper is to study the existence and the global exponential stability of the positive pseudo almost periodic solutions, which are more general and complicated than periodic and almost periodic solutions. Under suitable assumptions, and by using fixed point theorem, sufficient conditions are given to ensure that all solutions of this model converge exponentially to the positive pseudo almost periodic solution for the considered model. These results improve and extend some know

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11

Song, Na, Zheng-De Xia, and Qiang Hou. "The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients." Mathematica Slovaca 70, no. 2 (2020): 343–60. http://dx.doi.org/10.1515/ms-2017-0356.

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Abstract In this paper, we study the existence and global exponential stability of positive piecewise pseudo almost periodic solutions for the impulsive Lasota-Wazewska model with multiply time-varying delays when coefficients are piecewise pseudo almost periodic. Under proper conditions, by using the Gronwall’s inequation, we establish some criteria to ensure that the solution of this model stability exponentially to a positive piecewise pseudo almost periodic solution. Moreover, an example and its numerical simulation are given to illustrate the theoretical results.

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12

Koyuncuoglu, Halis Can, and Murat Adıvar. "Almost periodic solutions of Volterra difference systems." Demonstratio Mathematica 50, no. 1 (2017): 320–29. http://dx.doi.org/10.1515/dema-2017-0030.

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Abstract We study the existence of an almost periodic solution of discrete Volterra systems by means of fixed point theory. Using discrete variant of exponential dichotomy, we provide sufficient conditions for the existence of an almost periodic solution. Hence, we provide an alternative solution for the open problem proposed in the literature.

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13

Hamaya, Y., and T. Yoshizawa. "Almost periodic solutions in an integrodifferential equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 114, no. 1-2 (1990): 151–59. http://dx.doi.org/10.1017/s030821050002432x.

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SynopsisWe consider a system of integrodifferential equationswhere f(t, x) and F(t, s, x, y) are almost periodic in t uniformly for parameters, and we assume that the system has a bounded solution u(t). To discuss the existence of an almost periodic solution, we consider the relationship between the total stability of u(t) with respect to a certain metric ρ and the separation condition with respect to ρ. Moreover, we discuss a sufficient condition for the existence of a positive almost periodic solution of a model of the dynamics of an n-species system.

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14

Li, Yongkun, Xiaoli Huang, and Xiaohui Wang. "Weyl almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks with time-varying delays." AIMS Mathematics 7, no. 4 (2022): 4861–86. http://dx.doi.org/10.3934/math.2022271.

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<abstract><p>We consider the existence and stability of Weyl almost periodic solutions for a class of quaternion-valued shunting inhibitory cellular neural networks with time-varying delays. In order to overcome the incompleteness of the space composed of Weyl almost periodic functions, we first obtain the existence of a bounded continuous solution of the system under consideration by using the fixed point theorem, and then prove that the bounded solution is Weyl almost periodic by using a variant of Gronwall inequality. Then we study the global exponential stability of the Weyl al

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15

Qiu, Wenhua, and Jianguo Si. "Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/386812.

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This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution.

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16

Zhu, Ping. "Dynamics of the positive almost periodic solution to a class of recruitment delayed model on time scales." AIMS Mathematics 8, no. 3 (2023): 7292–309. http://dx.doi.org/10.3934/math.2023367.

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<abstract><p>By employing the operator theory, the Lyapunov function on time scales and the famous Gronwall's inequality, this paper addresses some dynamic properties of almost periodic solutions for a class of two species co-existence delayed model on time scales with almost periodic coefficients and Ricker, as well as the Beverton-Holt type function. First, we establish the existence and uniqueness of the almost periodic solution with a positive infimum by transforming the initial model into an equivalent integral equation. Second, we investigate the global exponential stability

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17

LI, YONGKUN, and TIANWEI ZHANG. "ALMOST PERIODIC SOLUTION FOR A DISCRETE HEMATOPOIESIS MODEL WITH TIME DELAY." International Journal of Biomathematics 05, no. 01 (2012): 1250003. http://dx.doi.org/10.1142/s179352451100143x.

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In this paper, we consider the discrete Hematopoiesis model with a time delay: [Formula: see text] Sufficient conditions for the existence of a unique uniformly asymptotically stable positive almost periodic solution are obtained by the work of [S. N. Zhang, G. Zheng, Almost periodic solutions of delay difference systems, Appl. Math. Comput.131 (2002) 497–516]. Some examples are considered to illustrate the main results.

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18

Zhang, Hui, Yingqi Li, Bin Jing, Xiaofeng Fang, and Jing Wang. "Almost Periodic Solution of a Discrete Schoener’s Competition Model with Delays." Journal of Difference Equations 2014 (July 24, 2014): 1–9. http://dx.doi.org/10.1155/2014/256094.

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We consider an almost periodic discrete Schoener’s competition model with delays. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result.

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19

Blot, Joël. "Calculus of variations in mean and convex Lagrangians, II." Bulletin of the Australian Mathematical Society 40, no. 3 (1989): 457–63. http://dx.doi.org/10.1017/s0004972700017524.

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We prove the Legendre Necessary Condition of the Calculus of Variations in Mean an arbitrary finite dimension. When the Lagrangian is convex, we establish that if the Euler-Lagrange equation possesses an almost periodic solution then it possesses periodic and constant solutions. We deduce from this fact various consequences on the structure of the set of almost periodic solutions.

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20

Xu, Shihe, Zuxing Xuan, and Fangwei Zhang. "Analysis of a free boundary problem for vascularized tumor growth with time delays and almost periodic nutrient supply." AIMS Mathematics 9, no. 5 (2024): 13291–312. http://dx.doi.org/10.3934/math.2024648.

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<abstract><p>In this research, we have proposed and investigated a time-delayed free boundary problem concerning tumor growth in the presence of almost periodic nutrient supply with angiogenesis. This study primarily focused on examining the impact of almost periodic nutrient supply, angiogenesis, and time delay on tumor growth dynamics. We analyzed the existence, uniqueness, and exponential stability of almost periodic solutions. Furthermore, we established conditions for the disappearance of almost periodic oscillations in tumors. The existence and uniqueness of almost periodic s

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21

Li, Yongkun, and Pan Wang. "Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales." Discrete & Continuous Dynamical Systems - S 10, no. 3 (2017): 463–73. http://dx.doi.org/10.3934/dcdss.2017022.

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22

Li, Yongkun, and Chao Wang. "Almost Periodic Functions on Time Scales and Applications." Discrete Dynamics in Nature and Society 2011 (2011): 1–20. http://dx.doi.org/10.1155/2011/727068.

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We first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. Based on these results, a class of high-order Hopfield neural networks with variable delays are studied on almost periodic time scales, and some sufficient conditions are established for the existence and global asymptotic stability of the almost periodic

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23

Zhang, Yi-Jin, and Chang-You Wang. "Stability analysis of n-species Lotka–Volterra almost periodic competition models with grazing rates and diffusions." International Journal of Biomathematics 07, no. 02 (2014): 1450011. http://dx.doi.org/10.1142/s1793524514500119.

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In this paper, almost periodic solution of a n-species Lotka–Volterra competition system with grazing rates and diffusions is investigated. By using the method of upper and lower solutions and Schauder fixed point theorem as well as Lyapunov stability theory, we give sufficient conditions under which the strictly positive space homogeneous almost periodic solution of the system is globally asymptotically stable. Moreover, some numerical simulations are given to validate our theoretical analysis.

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24

Hua, Ni, Tian Li-xin, and Liu Xun. "Positive Almost Periodic Solution on a Nonlinear Differential Equation." Mathematical Problems in Engineering 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/567319.

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We study the following nonlinear equationdx(t)/dt=x(t)[a(t)-b(t)xα(t)-f(t,x(t))]+g(t), by using fixed point theorem, the sufficient conditions of the existence of a unique positive almost periodic solution for above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the unique positive almost periodic solution are derived.

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25

Wang, Chao, Ravi P. Agarwal та Donal O’Regan. "δ-Almost Periodic Functions and Applications to Dynamic Equations". Mathematics 7, № 6 (2019): 525. http://dx.doi.org/10.3390/math7060525.

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In this paper, by employing matched spaces for time scales, we introduce a δ -almost periodic function and obtain some related properties. Also the hull equation for homogeneous dynamic equation is introduced and results of the existence are presented. In the sense of admitting exponential dichotomy for the homogeneous equation, the expression of a δ -almost periodic solution for a type of nonhomogeneous dynamic equation is obtained and the existence of δ -almost periodic solutions for new delay dynamic equations is considered. The results in this paper are valid for delay q-difference equatio

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26

Wang, Qinglong, and Zhijun Liu. "Uniformly Asymptotic Stability of Positive Almost Periodic Solutions for a Discrete Competitive System." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/182158.

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This paper is devoted to the study of almost periodic solutions of a discrete two-species competitive system. With the help of the methods of the Lyapunov function, some analysis techniques, and preliminary lemmas, we establish a criterion for the existence, uniqueness, and uniformly asymptotic stability of positive almost periodic solution of the system. Numerical simulations are presented to illustrate the analytical results.

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27

Wang, Chang-you, Rui-fang Wang, Ming Yi, and Rui Li. "Stability Analysis of Three-Species Almost Periodic Competition Models with Grazing Rates and Diffusions." Discrete Dynamics in Nature and Society 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/783136.

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Almost periodic solution of a three-species competition system with grazing rates and diffusions is investigated. By using the method of upper and lower solutions and Schauder fixed point theorem as well as Lyapunov stability theory, we give sufficient conditions to ensure the existence and globally asymptotically stable for the strictly positive space homogenous almost periodic solution, which extend and include corresponding results obtained by Q. C. Lin (1999), F. D. Chen and X. X. Chen (2003), and Y. Q. Liu, S. L, Xie, and Z. D. Xie (1996).

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Gao, Peng. "The solutions with recurrence property for stochastic linearly coupled complex cubic-quintic Ginzburg–Landau equations." Stochastics and Dynamics 19, no. 01 (2019): 1950005. http://dx.doi.org/10.1142/s0219493719500059.

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Stochastic periodic type solution is a powerful tool for studying qualitative analysis of stochastic dynamical systems. In this paper, we will establish the bounded solutions, stationary solutions, periodic solutions, almost periodic solutions, almost automorphic solutions for stochastic linearly coupled complex cubic-quintic Ginzburg–Landau equations under suitable conditions. The main novelty of this paper is dealing with cubic nonlinear terms and the quintic nonlinear terms which are not Lipschitz. We overcome this difficulty by the semigroup approach, stochastic analysis techniques, energy

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29

Gopalsamy, K. "Global asymptotic stability in an almost-periodic Lotka-Volterra system." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 27, no. 3 (1986): 346–60. http://dx.doi.org/10.1017/s0334270000004975.

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AbstractSufficient conditions are obtained for the existence of a globally asymptotically stable strictly positive (componentwise) almost-periodic solution of a Lotka-Volterra system with almost periodic coefficients.

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30

Yao, Zhijian. "Almost periodic solution of Nicholson’s blowflies difference equation with linear harvesting term." International Journal of Biomathematics 09, no. 04 (2016): 1650052. http://dx.doi.org/10.1142/s1793524516500522.

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This paper is concerned with Nicholson’s blowflies difference model with linear harvesting term. We obtain sufficient conditions for the existence of an almost periodic positive solution by using contraction mapping principle. The exponential convergence of almost periodic positive solution is derived by discrete Lyapunov functional.

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31

Rao, Aribindi Satyanarayan. "On annth-order infinitesimal generator and time-dependent operator differential equation with a strongly almost periodic solution." International Journal of Mathematics and Mathematical Sciences 32, no. 9 (2002): 573–78. http://dx.doi.org/10.1155/s0161171202108295.

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In a Banach space, ifuis a Stepanov almost periodic solution of a certainnth-order infinitesimal generator and time-dependent operator differential equation with a Stepanov almost periodic forcing function, thenu,u′,…,u (n−2)are all strongly almost periodic andu (n−1)is weakly almost periodic.

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32

Zhang, Hui, Bin Jing, Yingqi Li, and Xiaofeng Fang. "Global Analysis of Almost Periodic Solution of a Discrete Multispecies Mutualism System." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/107968.

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This paper discusses a discrete multispecies Lotka-Volterra mutualism system. We first obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of

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33

Wang, Li, Mei Yu, and Pengcheng Niu. "Periodic solution and almost periodic solution of impulsive Lasota–Wazewska model with multiple time-varying delays." Computers & Mathematics with Applications 64, no. 8 (2012): 2383–94. http://dx.doi.org/10.1016/j.camwa.2012.05.008.

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34

Meng, Xinzhu, and Lansun Chen. "Periodic solution and almost periodic solution for a nonautonomous Lotka–Volterra dispersal system with infinite delay." Journal of Mathematical Analysis and Applications 339, no. 1 (2008): 125–45. http://dx.doi.org/10.1016/j.jmaa.2007.05.084.

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35

Yao, Zhijian, Jehad Alzabut, and Debaldev Jana. "Dynamics of the Almost Periodic Discrete Mackey–Glass Model." Mathematics 6, no. 12 (2018): 333. http://dx.doi.org/10.3390/math6120333.

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This paper is concerned with a class of the discrete Mackey–Glass model that describes the process of the production of blood cells. Prior to proceeding to the main results, we prove the boundedness and extinction of its solutions. By means of the contraction mapping principle and under appropriate assumptions, we prove the existence of almost periodic positive solutions. Furthermore and by the implementation of the discrete Lyapunov functional, sufficient conditions are established for the exponential convergence of the almost periodic positive solution. Examples, as well as numerical simulat

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36

Chunhua, Feng. "Existence and Uniqueness of Positive Almost Periodic Solutions for a Class of Impulsive Lotka-Volterra Cooperation Models with Delays." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–8. https://doi.org/10.9734/BJMCS/2017/29723.

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This paper discusses an almost periodic Lotka-Volterra cooperation system with time delays and impulsive e ects. By constructing a suitable Lyapunov functional, a sucient condition which guarantees the existence, uniqueness and uniformly asymptotically stable of almost periodic solution of this system is obtained. A new result has been provided. A suitable example indicates the feasibility of the criterion.

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37

Huang, Xianying, and Yongkun Li. "Besicovitch almost periodic solutions for a stochastic generalized Mackey-Glass hematopoietic model." AIMS Mathematics 9, no. 10 (2024): 26602–30. http://dx.doi.org/10.3934/math.20241294.

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<p>This article aimed to investigate the existence and stability of Besicovitch almost periodic ($ B_{ap} $) positive solutions for a stochastic generalized Mackey-Glass hematopoietic model. To begin with, we used stochastic analysis theory, inequality techniques, and fixed point theorems to prove the existence and uniqueness of $ \mathcal{L}^p $-bounded and $ \mathcal{L}^p $-uniformly continuous positive solutions for the model under consideration. Then, we used definitions to prove that this unique positive solution is also a $ B_{ap} $ solution in finite-dimensional distributions. In

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38

Gao, Hongjun, and Charles Bu. "Almost periodic solution for a model of tumor growth." Applied Mathematics and Computation 140, no. 1 (2003): 127–33. http://dx.doi.org/10.1016/s0096-3003(02)00216-3.

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39

Ait Dads, E., and K. Ezzinbi. "Almost periodic solution for some neutral nonlinear integral equation." Nonlinear Analysis: Theory, Methods & Applications 28, no. 9 (1997): 1479–89. http://dx.doi.org/10.1016/s0362-546x(96)00012-0.

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40

Chen, Anping, and Jinde Cao. "Almost periodic solution of shunting inhibitory CNNs with delays." Physics Letters A 298, no. 2-3 (2002): 161–70. http://dx.doi.org/10.1016/s0375-9601(02)00469-3.

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41

Kondo, Shintaro. "On the almost-periodic solution of Hasegawa–Wakatani equations." Journal of Evolution Equations 16, no. 1 (2015): 155–72. http://dx.doi.org/10.1007/s00028-015-0296-0.

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42

Berger, M. S., and Y. Y. Chen. "Forced quasiperiodic and almost periodic solution for nonlinear systems." Nonlinear Analysis: Theory, Methods & Applications 21, no. 12 (1993): 949–65. http://dx.doi.org/10.1016/0362-546x(93)90118-c.

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43

Belokursky, M. S. "Periodic and almost periodic solutions of the Riccati equations with linear reflecting function." Doklady of the National Academy of Sciences of Belarus 66, no. 5 (2022): 479–88. http://dx.doi.org/10.29235/1561-8323-2022-66-5-479-488.

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The method of Mironenko’s reflecting function is used for investigation of Riccati equations. The class of Riccati equations with certain-type reflecting function has been preliminarily constructed. The necessary and sufficient conditions, under which the Riccati equation would have a reflecting function linear in phase variable, are proved. These conditions are constructive in nature, since on their basis the formula is obtained, which shows the linear in phase variable reflecting function in terms of the coefficients of the Riccati equation. Additionally, the relationship between the parity

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44

Yao, Zhijian. "Existence and exponential stability of almost periodic positive solution for host-macroparasite difference model." International Journal of Biomathematics 09, no. 02 (2016): 1650028. http://dx.doi.org/10.1142/s1793524516500285.

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This paper is concerned with a host-macroparasite difference model. By applying the contraction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investigate the exponential stability of almost periodic solution by means of Lyapunov functional.

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Rao, Aribindi Satyanarayan. "On first-order differential operators with Bohr-Neugebauer type property." International Journal of Mathematics and Mathematical Sciences 12, no. 3 (1989): 473–76. http://dx.doi.org/10.1155/s0161171289000608.

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We consider a differential equationddtu(t)-Bu(t)=f(t), where the functions u and f map the real line into a Banach space X and B: X→X is a bounded linear operator. Assuming that any Stepanov-bounded solution u is Stepanov almost-periodic when f is Bochner almost-periodic, we establish that any Stepanov-bounded solution u is Bochner almost-periodic when f is Stepanov almost-periodic. Some examples are given in which the operatorddt-B is shown to satisfy our assumption.

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Rao, Aribindi Satyanarayan. "On the stepanov almost periodic solution of a second-order infinitesimal generator differential equation." International Journal of Mathematics and Mathematical Sciences 14, no. 4 (1991): 757–61. http://dx.doi.org/10.1155/s0161171291001023.

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Lu, Lin, and Chaoling Li. "Almost Periodic Dynamics for Memristor-Based Shunting Inhibitory Cellular Neural Networks with Leakage Delays." Computational Intelligence and Neuroscience 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/3587271.

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We investigate a class of memristor-based shunting inhibitory cellular neural networks with leakage delays. By applying a new Lyapunov function method, we prove that the neural network which has a unique almost periodic solution is globally exponentially stable. Moreover, the theoretical findings of this paper on the almost periodic solution are applied to prove the existence and stability of periodic solution for memristor-based shunting inhibitory cellular neural networks with leakage delays and periodic coefficients. An example is given to illustrate the effectiveness of the theoretical res

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Abbas, S. "Pseudo Almost Periodic Sequence Solutions of Discrete Time Cellular Neural Networks." Nonlinear Analysis: Modelling and Control 14, no. 3 (2009): 283–301. http://dx.doi.org/10.15388/na.2009.14.3.14496.

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In this paper we discuss the existence and uniqueness of a k-pseudo almost periodic sequence solutions of a discrete time neural network. We give several sufficient conditions for the exponential and global attractivity of the solution.

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Yao, Zhijian. "Almost periodic solution of Nicholson's blowflies model with linear harvesting term and impulsive effects." International Journal of Biomathematics 08, no. 03 (2015): 1550053. http://dx.doi.org/10.1142/s1793524515500539.

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This paper is concerned with impulsive Nicholson's blowflies model with linear harvesting term. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential convergence of the almost periodic positive solution by Lyapunov functional.

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Wang, Zheng, and Yongkun Li. "Almost Periodic Solutions of a Discrete Mutualism Model with Feedback Controls." Discrete Dynamics in Nature and Society 2010 (2010): 1–18. http://dx.doi.org/10.1155/2010/286031.

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We consider a discrete mutualism model with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable.

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