Re: Coupled Chaotic Systems

From: Lou Pecora (pecora_at_anvil.nrl.navy.mil)
Date: 03/11/05

  • Next message: Conference Secretary: "CFP: International Conference on Intelligent Agents, Web Technologies and Internet Commerce" 
    Date: Fri, 11 Mar 2005 08:53:38 -0500

    In article <1110363959.345952.123130@o13g2000cwo.googlegroups.com>,
     "Gaurav Gandhi" <gaurav_cyber@hotmail.com> wrote:

    > Okay, let me start with the following specific query.
    >
    > In [1], it was shown that if several double scroll circuits are
    > connected unidirectionally in form of open / closed chain, then
    > depending upon the coupling parameter (called as stiffness coefficient)
    > the circuits are either synchronised to each other or they show
    > hyperchaotic behaviour.
    >
    > Is it possible to observe other phenomenons with this type of coupling
    > ?
    >
    > Question 2. How are waves / pattern formation related to chaotic
    > systems ? Also, is it specific to chaotic systems or even coupled
    > non-chaotic oscillators will also show same behaviour ?

    You can get some idea about patterns that come from synchronous states
    when they become unstable. You can check out,

    [1] "Synchronization Conditions and Desynchronizing Patterns in
    Coupled Limit-Cycle and Chaotic Systems," L.M. Pecora, Physical Review E
    58 (1), 347 (1998).

    [2] "Master Stability Functions for Synchronized Coupled Systems,"
    L.M. Pecora and T.L. Carroll, Physical Review Letters 80 (10), 2109
    (1998).

    I'm sure there are other papers out there that address this problem.
    The papers above emphasize chaotic systems, but similar analysis holds
    for most non-chaotic systems,too.

    The problem as treated in coupled systems is very similar to pattern
    formation problems in PDEs, e.g. reaction-diffusion equations. See work
    on Turing patterns/bifurcations. The coupled systems are similar to
    discrete versions of the PDEs, although somethings in the discrete
    versions may not show up in the PDEs and vice versa.

    But remember there may be other states that do not arise from the modes
    that grow when the synchronous state becomes unstable. Those may and
    often do depend on each individual system type. They are hard or
    impossible to predict for general classes of oscillators.

    -- Lou Pecora (my views are my own)

  • Next message: Conference Secretary: "CFP: International Conference on Intelligent Agents, Web Technologies and Internet Commerce"