Chaos-Based Communication Using Isochronal Synchronization: Considerations About the Synchronization Manifold

2020 ◽  
pp. 75-94
Author(s):  
J. M. V. Grzybowski ◽  
E. E. N. Macau ◽  
T. Yoneyama
Keyword(s):  
Synchronization Manifold

scholarly journals Multi-stable synchronization manifold in generalized synchronization of chaos

2008 ◽  
Vol 57 (5) ◽  
pp. 2761
Author(s):  
Yu Xiang ◽  
Zhu Shi-Jian ◽  
Liu Shu-Yong
Keyword(s):  
Generalized Synchronization ◽  
Synchronization Manifold

scholarly journals SYNCHRONIZATION IN NETWORKS OF SLIGHTLY NONIDENTICAL ELEMENTS

2008 ◽  
Vol 18 (03) ◽  
pp. 845-850 ◽  
Author(s):  
ALEXANDER E. HRAMOV ◽  
ANASTASIYA E. KHRAMOVA ◽  
ALEXEY A. KORONOVSKII ◽  
STEFANO BOCCALETTI
Keyword(s):  
Chaotic Systems ◽  
Invariant Solution ◽  
Mean Value ◽  
Noise Term ◽  
Original Distribution ◽  
The Mean ◽  
The Stability ◽  
Synchronization Manifold

We study synchronization processes in networks of slightly nonidentical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in parameters can be properly modeled by a noise term affecting the stability of the synchronous invariant solution emerging for identical systems when the parameter is set at the mean value of the original distribution.

scholarly journals STABILITY OF THE CONTROLLED SYNCHRONIZATION MANIFOLD IN A RING OF MUTUALLY COUPLED CHAOTIC SYSTEMS

2008 ◽  
Vol 18 (08) ◽  
pp. 2397-2414
Author(s):  
R. YAMAPI ◽  
M. A. AZIZ-ALAOUI
Keyword(s):  
Active Control ◽  
Chaotic Systems ◽  
Control Technique ◽  
Control Gain ◽  
Invariant Ring ◽  
Coupling Parameters ◽  
Single Oscillator ◽  
The Stability ◽  
Bifurcation Structures ◽  
Synchronization Manifold

The active control of the unstable synchronization manifold in a shift-invariant ring of N mutually coupled chaotic oscillators is investigated. After deriving the bifurcation structures and chaotic states in the single oscillator, we find the regime of coupling parameters leading to stable and unstable synchronization phenomena in the ring, using the Master stability function approach with the transverse Lyapunov exponents. The active control technique is applied on the mutually coupled chaotic systems to suppress unstable synchronization states. We derive the range of control gain parameters which leads to a successful control and the stability of the control design. The effects of the amplitude of the parametric perturbations on the stability boundaries of the controlled unstable synchronization process are also studied.

Invariance and stability conditions of interlayer synchronization manifold

2020 ◽  
Vol 101 (1) ◽  
Author(s):  
Sarbendu Rakshit ◽  
Bidesh K. Bera ◽  
Dibakar Ghosh
Keyword(s):  
Stability Conditions ◽  
Synchronization Manifold

scholarly journals Stability of the synchronization manifold in nearest neighbor nonidentical van der Pol-like oscillators

2010 ◽  
Vol 61 (1-2) ◽  
pp. 275-294 ◽  
Author(s):  
R. Yamapi ◽  
H. G. Enjieu Kadji ◽  
G. Filatrella
Keyword(s):  
Nearest Neighbor ◽  
Van Der Pol ◽  
Synchronization Manifold

SYNCHRONOUS AND ASYNCHRONOUS CHAOS IN COUPLED NEUROMODULES

1999 ◽  
Vol 09 (10) ◽  
pp. 1957-1968 ◽  
Author(s):  
FRANK PASEMANN
Keyword(s):  
Lyapunov Exponents ◽  
Computer Simulations ◽  
Chaotic Attractors ◽  
Discrete Dynamics ◽  
Stability Properties ◽  
Simulation Results ◽  
Synchronization Manifold

The parametrized time-discrete dynamics of two recurrently coupled neuromodules is studied analytically and by computer simulations. Conditions for the existence of synchronized dynamics are derived and periodic as well as quasiperiodic and chaotic attractors constrained to a synchronization manifold M are observed. Stability properties of the synchronized dynamics is discussed by using Lyapunov exponents parallel and transversal to the synchronization manifold. Simulation results are presented for selected sets of parameters. It is observed that locally stable synchronous dynamics often coexists with asynchronous periodic, quasiperiodic or even chaotic attractors.

GENERAL SYNCHRONIZATION OF GENESIO–TESI SYSTEMS

2004 ◽  
Vol 14 (01) ◽  
pp. 347-354 ◽  
Author(s):  
MAO-YIN CHEN ◽  
ZHENG-ZHI HAN ◽  
YUN SHANG
Keyword(s):  
Numerical Simulation ◽  
New Approach ◽  
Hurwitz Stability ◽  
The Stability ◽  
Synchronization Manifold

In this paper we develop a new approach to generally synchronize Genesio–Tesi systems. A suitable scalar signal of the master, Genesio–Tesi system, is transmitted to the slaver, which is derived from an iteration transformation of a Genesio–Tesi system. If a parameter is chosen properly, the stability of synchronization manifold becomes Hurwitz stability. Numerical simulation verifies the effectiveness of this method.

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