Delay-coupled discrete maps: Synchronization, bistability, and quasiperiodicity

Shrimali, Manish Dev; Sharan, Rangoli; Prasad, Awadhesh; Ramaswamy, Ramakrishna

doi:10.1016/j.physleta.2010.04.048

Cited by 7 publications

(5 citation statements)

References 24 publications

(25 reference statements)

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“…In addition to intermittency, time-delay systems are known to exhibit interesting dynamical features such as amplitude death [14,15], multistability [16] and quasiperiodicity [17]. In particular, recent theoretical [18] and experimental [19] studies have indicated various similarities between systems with long delays and spatio-temporal systems.…”

Section: Introductionmentioning

confidence: 99%

Intermittency in delay-coupled FitzHugh–Nagumo oscillators and loss of phase synchrony as its precursor

Saha¹,

Feudel²

2017

IASCS

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We study the dynamical properties of in-out intermittency in a system of two identical FitzHugh-Nagumo oscillators coupled by multiple time delays. In this system, the intermittency is manifested as irregular switching between a nearly synchronous state with small and large amplitude chaotic oscillations and a highly asynchronous state with a single large amplitude oscillation. We show that loss of phase synchrony significantly prior to the occurrence of the asynchronous large amplitude oscillation can be used as a precursor to the switching of states in such systems.

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Section: Introductionmentioning

confidence: 99%

Intermittency in delay-coupled FitzHugh–Nagumo oscillators and loss of phase synchrony as its precursor

Saha¹,

Feudel²

2017

IASCS

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“…The first systematic investigation of delay coupled phase oscillators was done by Schuster and Wagner 4 . Delay can give rise to some significant phenomena like synchronization [5][6][7] , multistability 8,9 and amplitude death 10,11 . Dissipative systems with time delayed feedback can generate high dimensional chaos and the dimension of chaotic attractor can be made larger by increasing delay time [12][13][14][15] .…”

Section: Introductionmentioning

confidence: 99%

Synchronization in a network of delay coupled maps with stochastically switching topologies

Nag

Poria

2016

Chaos, Solitons & Fractals

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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. Linear stability analysis of the synchronized state is done analytically for unit delay and the value of the critical coupling strength, at which the onset of synchronization occurs is determined analytically. The logistic map rx(1 − x) (a smooth unimodal map) is chosen for numerical simulation purpose. Synchronized steady state or synchronized period-2 orbit is stabilized for delay τ = 1. 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 the existence of synchronized chaos is confirmed. The results hold good for other smooth unimodal maps also.PACS numbers: 05.45.-a Due to the nonzero propagation speed of the transmitted signals the time delay in coupling arises in any system. Delay systems are in general infinite dimensional and can display complex dynamics and a very little is known about the basic relations between network structure and delay dynamics. Delay induced synchronization in coupled map lattice (CML) has already been discussed in many papers. However, in many systems (for example, communication, ecological, social and contact networks) links are not always active and the connectivity between the units changes (stochastically or deterministically) in time with a rate ranging from slow to fast. These facts motivates us to find out the effects of time delay in a CML having stochastically switching network topology. In a stochastically switching network connection between nodes changes randomly with time. Conditions for the stability of the synchronized steady state and periodic orbit are derived analytically using the properties of block circulant matrix. It is shown that in certain range of coupling (depending on probability of random connection) the CML synchronizes to periodic or chaotic orbit depending on delay time(τ ) and map parameters. In case of τ = 1 synchronized period − 2 is observed whereas for τ = 2 synchronized steady state and for higher values of τ synchronized chaos are observed.

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“…The physical mechanism underlying AD has also been extensively investigated [16][17][18][19]. For coupled oscillators on a regular lattice, mechanisms leading to AD may include oscillator mismatch [9,16], delayed coupling [20][21][22][23][24], asymmetric coupling [25][26][27], time-dependent coupling [28], conjugate coupling [29,30], nonlinear (nondiffusive) coupling [31], linear augmentation [32], and so on [33][34][35]. See a recent review [1] for more details, which gives the deep insight and many clues for understanding AD induced by different scenarios.…”

Section: Introductionmentioning

confidence: 99%

Mobility and density induced amplitude death in metapopulation networks of coupled oscillators

Shen

Chen

Hou

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate the effects of mobility and density on the amplitude death of coupled Landau-Stuart oscillators and Brusselators in metapopulation networks, wherein each node represents a subpopulation occupied any number of mobile individuals. By numerical simulations in scale-free topology, we find that the systems undergo phase transitions from incoherent state to amplitude death, and then to frequency synchronization with increasing the mobility rate or density of oscillators. Especially, there exists an extent of intermediate mobility rate and density that can lead to global oscillator death. Furthermore, we show that such nontrivial phenomena are robust to diverse network topologies. Our findings may invoke further efforts and attentions to explore the underlying mechanism of collective behaviors in coupled metapopulation systems.

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Delay-coupled discrete maps: Synchronization, bistability, and quasiperiodicity

Cited by 7 publications

References 24 publications

Intermittency in delay-coupled FitzHugh–Nagumo oscillators and loss of phase synchrony as its precursor

Intermittency in delay-coupled FitzHugh–Nagumo oscillators and loss of phase synchrony as its precursor

Synchronization in a network of delay coupled maps with stochastically switching topologies

Mobility and density induced amplitude death in metapopulation networks of coupled oscillators

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