Synchronization in a network of delay coupled maps with stochastically switching topologies
| Autor: | Mayurakshi Nag, Swarup Poria |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Steady state (electronics)
General Mathematics Applied Mathematics Synchronization of chaos Chaotic General Physics and Astronomy FOS: Physical sciences Statistical and Nonlinear Physics Lyapunov exponent Fixed point Network topology Topology Nonlinear Sciences - Chaotic Dynamics 01 natural sciences Synchronization 010305 fluids & plasmas symbols.namesake Control theory 0103 physical sciences symbols Logistic map Chaotic Dynamics (nlin.CD) 010306 general physics Mathematics |
| Popis: | The synchronization behavior of delay coupled chaotic smooth unimodal maps over a ring network with stochastic switching of links at every time step is reported in this paper. It is observed that spatiotemporal synchronization never appears for nearest neighbor connections; however, stochastic switching of connections with homogeneous delay (τ) is capable of synchronizing the network to homogeneous steady state or periodic orbit or synchronized chaotically oscillating state depending on the delay parameter, stochasticity parameter and map parameters. Most interestingly, linear stability analysis of the synchronized state is done analytically for unit delay and the value of the critical coupling strength, at which the synchronization occurs is determined analytically. The logistic map r x ( 1 − x ) (a smooth unimodal map) is chosen for numerical simulation purpose. It is found that synchronized steady state or synchronized period-2 orbit is stabilized for delay τ = 1 depending upon the nature of the local map. On the other hand for delay τ = 2 the network is stabilized to the fixed point of the local map. Numerical simulation results are in good agreement with the analytically obtained linear stability analysis results. Another interesting observation is the existence of synchronized chaos in the network for delay τ > 2. Calculating synchronization error and plotting time series data and Poincare first return map and largest Lyapunov exponent the existence of synchronized chaos is confirmed. The results hold good for other smooth unimodal maps also. |
| Databáze: | OpenAIRE |
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