On the detection of the generalized synchronization in the complex network with ring topology *

In this paper, the generalized synchronization in a complex network consisting of nodes being chaotic systems is studied. The main focus is on the applicability of the auxiliary system approach for the detection of the generalized synchronization phenomena in the complex networks with ring topology. It will be shown analytically and by numerical simulations that this method is applicable for the detection of the generalized synchronization in the unidirectional complex networks with nodes being the generalized Lorenz systems connected in a closed chain.

[1]  Shun-Yan Ren,et al.  Analysis and pinning control for generalized synchronization of delayed coupled neural networks with different dimensional nodes , 2018, J. Frankl. Inst..

[2]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[3]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Volodymyr Lynnyk,et al.  Synchronization of symmetric complex networks with heterogeneous time delays , 2019, 2019 22nd International Conference on Process Control (PC19).

[5]  V. A. Makarov,et al.  Delay-independent Synchronization in Ring Networks of Identical/Non-identical Systems with Transmission Delay Couplings , 2017 .

[6]  Arkady Pikovsky,et al.  On the interaction of strange attractors , 1984 .

[7]  Guanrong Chen,et al.  Robust synchronization of a class of chaotic networks , 2013, J. Frankl. Inst..

[8]  Kestutis Pyragas.  Conditional Lyapunov exponents from time series , 1997 .

[9]  S. Celikovsky,et al.  Observer-based chaos synchronization in the generalized chaotic Lorenz systems and its application to secure encryption , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[10]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[11]  Xiaoqun Wu,et al.  Inter-layer generalized synchronization of two-layer impulsively-coupled networks , 2019, Commun. Nonlinear Sci. Numer. Simul..

[12]  Ulrich Parlitz.  Detecting generalized synchronization , 2012 .

[13]  Alexander N. Pisarchik,et al.  Synchronization: From Coupled Systems to Complex Networks , 2018 .

[14]  Alexey A Koronovskii,et al.  Inapplicability of an auxiliary-system approach to chaotic oscillators with mutual-type coupling and complex networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  A. Pisarchik,et al.  Noise-induced quasiperiodicity in a ring of unidirectionally-coupled nonidentical maps , 2019, Physics Letters A.

[16]  Xiang Li,et al.  Fundamentals of Complex Networks: Models, Structures and Dynamics , 2015 .

[17]  Guanrong Chen,et al.  On a Generalized Lorenz Canonical Form of Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[18]  Guanrong Chen,et al.  Secure synchronization of a class of chaotic systems from a nonlinear observer approach , 2005, IEEE Transactions on Automatic Control.

[19]  M. Rabinovich,et al.  Stochastic synchronization of oscillation in dissipative systems , 1986 .

[20]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[21]  Toshiki Oguchi,et al.  Synchronization in Ring Networks of Systems with Transmission Delays , 2016 .

[22]  Zhigang Zheng,et al.  Transitions from partial to complete generalized synchronizations in bidirectionally coupled chaotic oscillators. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Alexander L. Fradkov,et al.  On synchronization in heterogeneous FitzHugh–Nagumo networks , 2019, Chaos, Solitons & Fractals.

[24]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Junan Lu,et al.  On Applicability of Auxiliary System Approach to Detect Generalized Synchronization in Complex Network , 2017, IEEE Transactions on Automatic Control.

[26]  Volodymyr Lynnyk,et al.  On applicability of auxiliary system approach in complex network with ring topology , 2019 .

[27]  Louis M Pecora,et al.  Synchronization of chaotic systems. , 2015, Chaos.

[28]  Michael Sebek,et al.  ANTI-SYNCHRONIZATION CHAOS SHIFT KEYING METHOD BASED ON GENERALIZED LORENZ SYSTEM , 2006 .

[29]  Volodymyr Lynnyk,et al.  On detection of generalized synchronization in the complex network with ring topology via the duplicated systems approach* , 2019, 2019 8th International Conference on Systems and Control (ICSC).

[30]  A. Prasad,et al.  Generalized synchronization in a conservative and nearly conservative systems of star network. , 2018, Chaos.

[31]  Yuhua Xu,et al.  Inferring topologies via driving-based generalized synchronization of two-layer networks , 2015, 1512.02358.

[32]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[33]  Volodymyr Lynnyk,et al.  Synchronization of nonlinear complex networks with input delays and minimum-phase zero dynamics , 2019, 2019 19th International Conference on Control, Automation and Systems (ICCAS).