Rössler-network with time delay: Univariate impulse pinning synchronization.

Rössler had a brilliant and successful life as a scientist during which he published a benchmark dynamical system by using an electronic circuit interpreting chemical reactions. This is our contribution to honor his splendid erudite career. It is a hot topic to regulate a network behavior using the pinning control with respect to a small set of nodes in the network. Besides pinning to a small number of nodes, small perturbation to the node dynamics is also demanded. In this paper, the pinning synchronization of a coupled Rössler-network with time delay using univariate impulse control is investigated. Using the Lyapunov theory, a theorem is proved for the asymptotic stability of synchronization in the network. Simulation is given to validate the correctness of the analysis and the effectiveness of the proposed univariate impulse pinning controller.

[1]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[2]  Tingwen Huang,et al.  Impulsive stabilization and synchronization of a class of chaotic delay systems. , 2005, Chaos.

[3]  M. Cross,et al.  Pinning control of spatiotemporal chaos , 1997, chao-dyn/9705001.

[4]  Yi Zhao,et al.  Pinning synchronization for reaction-diffusion neural networks with delays by mixed impulsive control , 2019, Neurocomputing.

[5]  Junan Lu,et al.  Pinning adaptive synchronization of a general complex dynamical network , 2008, Autom..

[6]  Yan Wang,et al.  Synchronization of nonlinearly coupled complex networks: Distributed impulsive method , 2020 .

[7]  Celso Grebogi,et al.  Weak connections form an infinite number of patterns in the brain , 2017, Scientific Reports.

[8]  Chao Bai,et al.  Double-Sub-Stream M-ary Differential Chaos Shift Keying Wireless Communication System Using Chaotic Shape-Forming Filter , 2020, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Liu Ding,et al.  Anticontrol of chaos via direct time delay feedback , 2006 .

[10]  Jinde Cao,et al.  Pinning impulsive stabilization of nonlinear Dynamical Networks with Time-Varying Delay , 2012, Int. J. Bifurc. Chaos.

[11]  Jie Liu,et al.  Synchronization in duplex networks of coupled Rössler oscillators with different inner-coupling matrices , 2020, Neurocomputing.

[12]  Chao Bai,et al.  Synchronization of Hyperchaos With Time Delay Using Impulse Control , 2020, IEEE Access.

[13]  Christophe Letellier,et al.  Nonlinear graph-based theory for dynamical network observability. , 2018, Physical review. E.

[14]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[15]  O. Rössler,et al.  Hyperchaos of arbitrary order generated by a single feedback circuit, and the emergence of chaotic walks. , 2004, Chaos.

[16]  L. A. Aguirre,et al.  Controllability and synchronizability: Are they related? , 2016 .

[17]  I. Bodale,et al.  Chaos control for Willamowski–Rössler model of chemical reactions , 2015 .

[18]  J. Munkres.  ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[19]  Lacra Pavel,et al.  Dynamics and stability in optical communication networks: a system theory framework , 2004, Autom..

[20]  J..  CHAOTIC ATTRACTORS OF AN INFINITE-DIMENSIONAL DYNAMICAL SYSTEM , 2002 .

[21]  Celso Grebogi,et al.  Hyperchaos synchronization using univariate impulse control. , 2019, Physical review. E.

[22]  Qingdu Li,et al.  A topological horseshoe in the hyperchaotic Rossler attractor , 2008 .

[23]  Jianwu Dang,et al.  Plaintext-related image encryption algorithm based on perceptron-like network , 2020, Inf. Sci..

[24]  Celso Grebogi,et al.  Dynamics of delay induced composite multi-scroll attractor and its application in encryption , 2017 .

[25]  Harold W. Kuhn,et al.  The Hungarian method for the assignment problem , 1955, 50 Years of Integer Programming.

[26]  Hai-Peng Ren,et al.  License plate recognition using complex network feature , 2014, Proceeding of the 11th World Congress on Intelligent Control and Automation.

[27]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[28]  Jinde Cao,et al.  Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control , 2017, Neural Networks.

[29]  Xinzhi Liu,et al.  Uniform asymptotic stability of impulsive delay differential equations , 2001 .

[30]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[31]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  Jinde Cao,et al.  Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller , 2013, SIAM J. Control. Optim..

[33]  O. Rössler.  An equation for hyperchaos , 1979 .