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Gotowe bibliografie tematyczne / Fractional chaotic system

Gotowa bibliografia na temat „Fractional chaotic system”

Autor: Grafiati

Data publikacji: 16 marca 2023

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Artykuły w czasopismach na temat "Fractional chaotic system":

1

Yang, Chunde, Hao Cai i Ping Zhou. "Compound Generalized Function Projective Synchronization for Fractional-Order Chaotic Systems". Discrete Dynamics in Nature and Society 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/7563416.

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A modified function projective synchronization for fractional-order chaotic system, called compound generalized function projective synchronization (CGFPS), is proposed theoretically in this paper. There are one scaling-drive system, more than one base-drive system, and one response system in the scheme of CGFPS, and the scaling function matrices come from multidrive systems. The proposed CGFPS technique is based on the stability theory of fractional-order system. Moreover, we achieve the CGFPS between three-driver chaotic systems, that is, the fractional-order Arneodo chaotic system, the fractional-order Chen chaotic system, and the fractional-order Lu chaotic system, and one response chaotic system, that is, the fractional-order Lorenz chaotic system. Numerical experiments are demonstrated to verify the effectiveness of the CGFPS scheme.

2

Hu, Jian-Bing, i Ling-Dong Zhao. "Finite-Time Synchronizing Fractional-Order Chaotic Volta System with Nonidentical Orders". Mathematical Problems in Engineering 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/264136.

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We investigate synchronizing fractional-order Volta chaotic systems with nonidentical orders in finite time. Firstly, the fractional chaotic system with the same structure and different orders is changed to the chaotic systems with identical orders and different structure according to the property of fractional differentiation. Secondly, based on the lemmas of fractional calculus, a controller is designed according to the changed fractional chaotic system to synchronize fractional chaotic with nonidentical order in finite time. Numerical simulations are performed to demonstrate the effectiveness of the method.

3

Zhou, Ping, i Rui Ding. "An Adaptive Tracking Control of Fractional-Order Chaotic Systems with Uncertain System Parameter". Mathematical Problems in Engineering 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/521549.

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An adaptive tracking control scheme is presented for fractional-order chaotic systems with uncertain parameter. It is theoretically proved that this approach can make the uncertain parameter fractional-order chaotic system track any given reference signal and the uncertain system parameter is estimated through the adaptive tracking control process. Furthermore, the reference signal may belong to other integer-orders chaotic system or belong to different fractional-order chaotic system with different fractional orders. Two examples are presented to demonstrate the effectiveness of the proposed method.

4

EL-KHAZALI, REYAD, WAJDI AHMAD i YOUSEF AL-ASSAF. "SLIDING MODE CONTROL OF GENERALIZED FRACTIONAL CHAOTIC SYSTEMS". International Journal of Bifurcation and Chaos 16, nr 10 (październik 2006): 3113–25. http://dx.doi.org/10.1142/s0218127406016719.

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A sliding mode control technique is introduced for generalized fractional chaotic systems. These systems are governed by a set of fractional differential equations of incommensurate orders. The proposed design method relies on the fact that the stability region of a fractional system contains the stability region of its underlying integer-order model. A sliding mode controller designed for an equivalent integer-order chaotic system is used to stabilize all its corresponding fractional chaotic systems. The design technique is demonstrated using two generalized fractional chaotic models; a chaotic oscillator and the Chen system. The effect of the total fractional order is investigated with respect to the controller effort and the convergence rate of the system response to the origin. Numerical simulations validate the main results of this work.

5

Niu, Yujun, Xuming Sun, Cheng Zhang i Hongjun Liu. "Anticontrol of a Fractional-Order Chaotic System and Its Application in Color Image Encryption". Mathematical Problems in Engineering 2020 (12.03.2020): 1–12. http://dx.doi.org/10.1155/2020/6795964.

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This paper investigates the anticontrol of the fractional-order chaotic system. The necessary condition of the anticontrol of the fractional-order chaotic system is proposed, and based on this necessary condition, a 3D fractional-order chaotic system is driven to two new 4D fractional-order hyperchaotic systems, respectively, without changing the parameters and fractional order. Hyperchaotic properties of these new fractional dynamic systems are confirmed by Lyapunov exponents and bifurcation diagrams. Furthermore, a color image encryption algorithm is designed based on these fractional hyperchaotic systems. The effectiveness of their application in image encryption is verified.

6

WANG, XING-YUAN, GUO-BIN ZHAO i YU-HONG YANG. "DIVERSE STRUCTURE SYNCHRONIZATION OF FRACTIONAL ORDER HYPER-CHAOTIC SYSTEMS". International Journal of Modern Physics B 27, nr 11 (25.04.2013): 1350034. http://dx.doi.org/10.1142/s0217979213500343.

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This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor–corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient.

7

Jiang, Cuimei, Shutang Liu i Chao Luo. "A New Fractional-Order Chaotic Complex System and Its Antisynchronization". Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/326354.

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We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme.

8

Fang, Jing, i Ruo Xun Zhang. "Synchronization of Incommensurate Fractional-Order Chaotic System Using Adaptive Control". Applied Mechanics and Materials 602-605 (sierpień 2014): 946–49. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.946.

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This paper investigates the synchronization of incommensurate fractional-order chaotic systems, and proposes a modified adaptive-feedback controller for fractional-order chaos synchronization based on Lyapunov stability theory, fractional order differential inequality and adaptive control theory. This synchronization approach that is simple, global and theoretically rigorous enables synchronization of fractional-order chaotic systems be achieved in a systematic way. Simulation results for a fractional-order chaotic system is provided to illustrate the effectiveness of the proposed scheme.

9

Zhou, Ping, Rui Ding i Yu-xia Cao. "Hybrid Projective Synchronization for Two Identical Fractional-Order Chaotic Systems". Discrete Dynamics in Nature and Society 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/768587.

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A hybrid projective synchronization scheme for two identical fractional-order chaotic systems is proposed in this paper. Based on the stability theory of fractional-order systems, a controller for the synchronization of two identical fractional-order chaotic systems is designed. This synchronization scheme needs not to absorb all the nonlinear terms of response system. Hybrid projective synchronization for the fractional-order Chen chaotic system and hybrid projective synchronization for the fractional-order hyperchaotic Lu system are used to demonstrate the validity and feasibility of the proposed scheme.

10

Cui, Yan, Hongjun He, Guan Sun i Chenhui Lu. "Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization". Advances in Mathematical Physics 2019 (3.07.2019): 1–12. http://dx.doi.org/10.1155/2019/3713789.

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In this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure. We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. The complexity of fractional order chaotic system is given by spectral entropy algorithm andC0algorithm. We concluded that the fractional order chaotic system has a higher complexity. The fractional order system can generate rich dynamic behavior phenomenon with the values of the parameters and the order changed. We applied the finite time stability theory to design the finite time synchronous controller between drive system and corresponding system. The numerical simulations demonstrate that the controller provides fast and efficient method in the synchronization process.

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Rozprawy doktorskie na temat "Fractional chaotic system":

1

Rahman, Z. A. S. A., B. H. Jasim, Yasir Al-Yasir, Raed A. Abd-Alhameed i B. N. Alhasnawi. "A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization and Its Digital Implementation". MDPI, 2021. http://hdl.handle.net/10454/18546.

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yes
In this paper, a new fractional order chaotic system without equilibrium is proposed, analyti-cally and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigation were used to describe the system dynamical behaviors including, the system equilibria, the chaotic attractors, the bifurcation diagrams and the Lyapunov expo-nents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attrac-tors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive con-trol theory has been developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state varia-bles for the master and slave. Consequently, the update laws of the slave parameters are ob-tained, where the slave parameters are assumed to be uncertain and estimate corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results are obtained by MATLAB and the Arduino Due boards respectively, where a good consistent between the simulation results and the ex-perimental results. indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

2

Yang, Chunxiao. "Fractional chaotic pseudo-random number generator design and application to image cryptosystem". Electronic Thesis or Diss., Ecole centrale de Nantes, 2022. http://www.theses.fr/2022ECDN0063.

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Dans cette thèse, nous avons utilisé des systèmes chaotiques pour concevoir des générateurs de nombres pseudoaléatoires(PRNG) et appliqué ces derniers aux cryptosystèmes en raison de leurs caractéristiques prometteuses, telles que le caractèrealéatoire et la sensibilité aux conditions initiales. Les systèmes chaotiques fractionnaires, bien que moins discutés que les carteset systèmes chaotiques classiques d’ordre entier, possèdent une complexité inhérente qui apporte de la nouveauté, de la complexité et des clés secrètes supplémentaires à la conception Chaotic PRNG (CPRNG), qui à son tour améliore la sécurité du cryptosystème. Cette thèse a étudié les différentes approches de calcul numérique pour les systèmes chaotiques fractionnaires. Une méthode de calcul utilisant une grille non uniforme avec deux compositions de grille différentes a été proposée pour résoudre numériquement les systèmes chaotiques fractionnaires 3D. Les CPRNG Fractionnaires (FCPRNG), qui répondent aux exigences aléatoires et statistiques, ont été conçus pour la première fois en utilisant trois systèmes chaotiques fractionnaires différents. De plus, un chiffrement par flux et un chiffrement par blocs basés sur des méthodes de codage et de décodage de l’ADN ont été proposés et étudiés à l’aide des FCPRNG conçus. Les deux schémas de chiffrements ont été vérifiés comme étant sûrs et fiables
Chaotic systems have been employed to design pseudo-random number generators (PRNG) and applied to cryptosystems due to their promising features, such as randomness and sensitivity to initial conditions. The fractional chaotic systems, though muchless discussed than the classical integer order chaotic maps and systems, possess intriguing intricacy which can provide novelty, complexity, and extra secret keys to the Chaotic PRNG (CPRNG) design, which in turn enhance the security of the cryptosystem.This thesis investigated different numerical calculation approaches for fractional chaotic systems. A non-uniform gird calculationmethod with two different grid compositions was proposed to solve the 3D fractional chaotic systems numerically. The FractionalCPRNGs (FCPRNG), which meet the randomness and statistical requirements, were designed for the first time employing threedifferent fractional chaotic systems. In addition, a stream cipher and a block cipher based on DNA encoding and decoding methods were proposed and studied using the designed FCPRNGs. Both ciphers have been verified to be secure and reliable

3

Beig, Mirza Tanweer Ahmad. "Fractional Calculus and Dynamic Approach to Complexity". Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc822832/.

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Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. Nonlinear Langevin equation describes the mean field of a finite size complex network at criticality. Critical phenomena and temporal complexity are two very important issues of modern nonlinear dynamics and the link between them found by the author can significantly improve the understanding behavior of dynamical systems at criticality. The subject of temporal complexity addresses the challenging and especially helpful in addressing fundamental physical science issues beyond the limits of reductionism.

4

Yang, Kung-Wei, i 楊坤偉. "Chaos and chaos synchronization of integral and fractional order unified chaotic system". Thesis, 2005. http://ndltd.ncl.edu.tw/handle/53991815856211994860.

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Chang, Shuo-Wen, i 張碩文. "Uncertain Fractional Order Chaotic System Synchronization Based on Adaptive Intelligent Control via LMI Approach：Indirect；Direct；Hybrid". Thesis, 2011. http://ndltd.ncl.edu.tw/handle/71061366396479798113.

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碩士
逢甲大學
電子工程所
99
This thesis presents an adaptive fuzzy control for uncertain fractional order chaotic system via linear matrices inequality (LMI) approach incorporating Lyapunov stability method with H∞ control to deal with the training data corrupted by noise and rule uncertainties involving external disturbance. The adaptive intelligent fuzzy control which includes direct, indirect and hybrid categories is developed for a class of uncertain fractional order chaotic system synchronization and uncertain fractional order chaotic system with time delay synchronization. The hybrid adaptive fuzzy controller is a combination of direct and indirect adaptive fuzzy controllers. A weighting factor, which can be adjusted by the trade-off between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive fuzzy controller and direct adaptive fuzzy controller. Nonlinear fractional chaotic slave system is gully illustrated to track the trajectory generated from fractional order master chaotic system. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Simulation results show that the interval type-2 adaptive fuzzy logic controllers (AFLCs) can effectively handle the training data corrupted by external disturbance, internal noise and rule uncertainties involving external disturbance. Comparing with interval type-2 AFLCs, type-1 AFLCs not only expend more control effort to deal with the training data corrupted by noises but also obtain worse synchronization performance.

6

Sibiya, Abram Hlophane. "Numerical methods for a four dimensional hyperchaotic system with applications". Diss., 2019. http://hdl.handle.net/10500/26398.

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This study seeks to develop a method that generalises the use of Adams-Bashforth to solve or treat partial differential equations with local and non-local differentiation by deriving a two-step Adams-Bashforth numerical scheme in Laplace space. The resulting solution is then transformed back into the real space by using the inverse Laplace transform. This is a powerful numerical algorithm for fractional order derivative. The error analysis for the method is studied and presented. The numerical simulations of the method as applied to the four-dimensional model, Caputo-Lu-Chen model and the wave equation are presented. In the analysis, the bifurcation dynamics are discussed and the periodic doubling processes that eventually caused chaotic behaviour (butterfly attractor) are shown. The related graphical simulations that show the existence of fractal structure that is characterised by chaos and usually called strange attractors are provided. For the Caputo-Lu-Chen model, graphical simulations have been realised in both integer and fractional derivative orders.
Mathematical Sciences
M. Sc. (Applied Mathematics)

7

Chien, Tseng-Hsu, i 錢增旭. "Low-Order State-Space Self-Tuning Control for Stochastic Integer/Fractional Order Chaotic Systems and Fault Tolerant Control". Thesis, 2006. http://ndltd.ncl.edu.tw/handle/03730441677592432830.

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博士
國立成功大學
電機工程學系碩博士班
95
A study of a new effective low-order state-space self-tuning control for stochastic integer/fractional order chaotic systems and fault tolerant control is presented in this dissertation. This dissertation includes three aspects: First of all, an effective lower-order tuner for a stochastic chaotic hybrid system is designed using the observer/Kalman filter identification method, in which the system state in a general coordinate form is transformed to one in an observer form. Moreover, it provides a lower-order realization of the tracker, with computationally effective initialization, for on-line “auto-regressive moving average process with exogenous model-based” identification and a lower-order state-space self-tuning control technique. Secondly, based on the modified state-space self-tuning control, a novel low-order tuner via the observer/Kalman filter identification is proposed for stochastic fractional-order chaotic systems. Then, in stead of using the conventional identification algorithm used in self-tuning control, the Kalman filter as a parameter estimator with the state-space innovation form is presented for effectively estimating the time-varying parameters. Besides, taking the advantage of the digital redesign approach, the current-output-based observer is proposed for the modified self-tuning control. Finally, a new low-order self-tuning fault-tolerant control scheme for unknown multivariable stochastic systems by modifying the conventional self-tuning control is also developed. For the detection of fault occurrence, a quantitative criterion is developed by comparing the innovation process errors occurring in the Kalman filter estimation algorithm. The proposed method can effectively cope with partially abrupt and/or gradual system faults and/or input failures with fault detection.

8

Lee, Tun-Yuan, i 李敦元. "Chaos Synchronization of Uncertain Fractional Order Chaotic Systems Based on Adaptive Fuzzy Sliding Mode Control: Indirect; Direct; Hybrid". Thesis, 2011. http://ndltd.ncl.edu.tw/handle/55228805426400138229.

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碩士
逢甲大學
電子工程所
99
This thesis proposes an adaptive fuzzy sliding model controller (AFSMC) to synchronize two different uncertain fractional order chaotic systems and to synchronize two different uncertain fractional order time delay chaotic systems which are infinite dimensional in nature and time delay is a source of instability. Because modeling the behavior of dynamical systems by fractional order differential equations has more advantages than integer order modeling, the adaptive time delay fuzzy logic system is constructed to approximate the unknown fractional order time delay system functions. The AFSMC is classified into three categories: direct AFSMC, indirect AFSMC and hybrid AFSMC. A hybrid AFSMC can be constructed by incorporating both fuzzy description and fuzzy control rules using a weighting factor a to sum together the control efforts from indirect AFSMC and direct AFSMC. The weighting factor a [0, 1] can be adjusted by the trade-off between plant knowledge and control knowledge. We let a=1 if pure indirect adaptive FNN controller is required and a=0 when pure direct adaptive FNN controller is chosen. If fuzzy control rules are more important and reliable than fuzzy descriptions of the plant, choose smaller a; otherwise choose larger a. By using Lyapunov stability criterion, the free parameters of the adaptive fuzzy controller can be tuned on line by output feedback control law and adaptive law. The sliding model design procedure not only guarantees the stability and robustness of the proposed AFSMC, but also the external disturbance on the synchronization error can be attenuated. The simulation example is included to confirm validity and synchronization performance of the advocated design methodology.

Książki na temat "Fractional chaotic system":

1

Azar, Ahmad Taher, Sundarapandian Vaidyanathan i Adel Ouannas, red. Fractional Order Control and Synchronization of Chaotic Systems. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50249-6.

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Martínez-Guerra, Rafael, Claudia A. Pérez-Pinacho i Gian Carlo Gómez-Cortés. Synchronization of Integral and Fractional Order Chaotic Systems. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15284-4.

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3

Sun, Kehui, Shaobo He i Huihai Wang. Solution and Characteristic Analysis of Fractional-Order Chaotic Systems. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3273-1.

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Azar, Ahmad Taher, Sundarapandian Vaidyanathan i Adel Ouannas. Fractional Order Control and Synchronization of Chaotic Systems. Springer, 2018.

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Azar, Ahmad Taher, Sundarapandian Vaidyanathan i Adel Ouannas. Fractional Order Control and Synchronization of Chaotic Systems. Springer, 2017.

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Zaslavsky, George M. Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, Incorporated, 2004.

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Zaslavsky, George M. Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, USA, 2005.

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Zaslavsky, George M. Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, 2008.

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He, Shaobo, Huihai Wang i Kehui Sun. Solution and Characteristic Analysis of Fractional-Order Chaotic Systems. Springer, 2022.

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Boulkroune, Abdesselem, i Samir Ladaci. Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems. IGI Global, 2018.

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Części książek na temat "Fractional chaotic system":

1

Yang, Chunxiao, Ina Taralova i Jean Jacques Loiseau. "Fractional Chaotic System Solutions and Their Impact on Chaotic Behaviour". W 14th Chaotic Modeling and Simulation International Conference, 521–35. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-96964-6_36.

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Sun, Kehui, Shaobo He i Huihai Wang. "Complexity Analysis of Fractional-Order Chaotic System". W Solution and Characteristic Analysis of Fractional-Order Chaotic Systems, 117–41. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3273-1_7.

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Bhalekar, Sachin. "Dynamics of Fractional Order Complex Uçar System". W Fractional Order Control and Synchronization of Chaotic Systems, 747–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50249-6_26.

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Feng, Junqing, i Guohong Liang. "Dynamical Analysis of Fractional-Order Hyper-chaotic System". W Advances in Intelligent Systems and Computing, 36–41. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-69096-4_5.

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Razmjou, E. G., A. Ranjbar, Z. Rahmani i R. Ghaderi. "Robust Synchronization and Parameter Identification of a Unified Fractional-Order Chaotic System". W Fractional Dynamics and Control, 173–84. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0457-6_14.

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Martínez-Guerra, Rafael, Claudia A. Pérez-Pinacho i Gian Carlo Gómez-Cortés. "Synchronization of an Uncertain Rikitake System with Parametric Estimation". W Synchronization of Integral and Fractional Order Chaotic Systems, 101–10. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15284-4_5.

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Vaidyanathan, Sundarapandian, Quanmin Zhu i Ahmad Taher Azar. "Adaptive Control of a Novel Nonlinear Double Convection Chaotic System". W Fractional Order Control and Synchronization of Chaotic Systems, 357–85. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50249-6_12.

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Lassoued, Abir, i Olfa Boubaker. "A New Fractional-Order Jerk System and Its Hybrid Synchronization". W Fractional Order Control and Synchronization of Chaotic Systems, 699–718. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50249-6_24.

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Lamamra, Kheireddine, Sundarapandian Vaidyanathan, Ahmad Taher Azar i Chokri Ben Salah. "Chaotic System Modelling Using a Neural Network with Optimized Structure". W Fractional Order Control and Synchronization of Chaotic Systems, 833–56. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50249-6_29.

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Ben Saad, Afef, i Olfa Boubaker. "A New Fractional-Order Predator-Prey System with Allee Effect". W Fractional Order Control and Synchronization of Chaotic Systems, 857–77. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50249-6_30.

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Streszczenia konferencji na temat "Fractional chaotic system":

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Donato, Cafagna, i Grassi Giuseppe. "A novel memristor-based chaotic system with fractional order". W 2014 International Conference on Fractional Differentiation and its Applications (ICFDA). IEEE, 2014. http://dx.doi.org/10.1109/icfda.2014.6967415.

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Liu, Licai, Chuanhong Du, Fengxia Zhu i Liangli Xiu. "Multi-System Fractional-Order Chaotic Signal Generator". W 2019 IEEE 2nd International Conference on Electronics Technology (ICET). IEEE, 2019. http://dx.doi.org/10.1109/eltech.2019.8839428.

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Naseri, E., A. Ranjbar i S. H. HosseinNia. "Backstepping Control of Fractional-Order Chen System". W ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86950.

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Streszczenie:

In this paper, Chaos and its control is studied in fractional-order Chen system. Backstepping method is proposed to synchronize two identical fractional-order Chen systems. The simulation results show that this method can effectively synchronize two identical chaotic systems.