Memory matters in synchronization of stochastically coupled maps

Maurizio Porfiri, Igor Belykh

Research output: Contribution to journalArticle

Abstract

Synchronization of stochastically coupled chaotic oscillators is a topic of intensive research for its ubiquitous application across natural and technological systems. Several breakthroughs have been made over the last decade in understanding the underpinnings of stochastic synchronization. Yet, most of the literature has focused on memoryless switching, where the coupling between the oscillators intermittently changes independently of the switching history. Here, we analytically investigate the synchronization of two one-dimensional coupled nonlinear maps under Markovian switching. We linearize the system in the vicinity of the synchronous solution and examine the mean square asymptotic stability of the error dynamics. By leveraging state-of-the-art techniques in jump linear systems, fundamentals of ergodic theory, and perturbation analysis, we elucidate the potential of Markovian switching in manipulating the stability of synchronization. We focus on chaotic tent maps, for which we compute exact, closed-form expressions to measure the error dynamics. The hypothesis of memoryless switching has often been challenged in practical applications; this study makes a first, necessary step toward unraveling the role of switching memory in stochastic synchronization.

Original languageEnglish (US)
Pages (from-to)1372-1396
Number of pages25
JournalSIAM Journal on Applied Dynamical Systems
Volume16
Issue number3
DOIs
StatePublished - 2017

Fingerprint

Coupled Maps
Synchronization
Data storage equipment
Markovian Switching
Jump Linear Systems
Tent Map
Mean-square Stability
Nonlinear Map
Chaotic Oscillator
Ergodic Theory
Chaotic Map
Perturbation Analysis
Coupled Oscillators
Asymptotic Stability
Asymptotic stability
Closed-form
Linear systems
Necessary

Keywords

  • Chaos
  • Lyapunov exponent
  • Markov process
  • Mean square stability
  • Switching

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation

Cite this

Memory matters in synchronization of stochastically coupled maps. / Porfiri, Maurizio; Belykh, Igor.

In: SIAM Journal on Applied Dynamical Systems, Vol. 16, No. 3, 2017, p. 1372-1396.

Research output: Contribution to journalArticle

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