Synchronization of Irregular Complex Networks with Chaotic Oscillators: Hamiltonian Systems Approach

 

C. Posadas-Castillo*¹, E. Garza-González¹, D.A. Díaz-Romero¹, E. Alcorta-García¹ and C. Cruz-Hernández²

 

¹ Universidad Autónoma de Nuevo León, Facultad de Ingeniería Mecánica y Eléctrica, México.

² Centro de Investigación Científica y de Educación Superior de Ensenada, México. *cornelio.posadascs@uanl.edu.mx

 

ABSTRACT

Synchronization of multiple chaotic oscillators in Hamiltonian form is numerically studied and is achieved by appealing to complex systems theory [1-5]. The topology that we consider is the irregular coupled network. Two cases are considered: i) chaotic synchronization without master oscillator (where the final collective behaviour is a new chaotic state) and ii) chaotic synchronization with master oscillator (where the final collective behaviour is imposed by the dynamics of the master oscillator to multiple slave oscillators). The Hysteretic and Róssler chaotic oscillators in Hamiltonian form will be used as examples.

Keywords: Synchronization, Complex Networks, Hamiltonian Systems.

 

RESUMEN

La sincronización de múltiples osciladores caóticos en forma Hamiltoniana es numéricamente estudiada y se logra apelando a la teoría de sistemas complejos [1-5]. La topología que consideramos es la red compleja irregular. Dos casos se consideran: i) sincronización caótica sin oscilador maestro (donde el comportamiento colectivo final de la red compleja es un estado caótico nuevo y ii) sincronización caótica con oscilador maestro (donde el comportamiento colectivo final de la red caótica es impuesto por la dinámica del oscilador maestro a los osciladores esclavos). Los osciladores caóticos de Róssler e Histéresis en forma Hamiltoniana se utilizan como ejemplos.

 

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Acknowledgment

This work was supported by CONACYT, México under Research Grant No. 166654 and by FIME-UANL.

 

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