Frequency discontinuity and amplitude death with time-delay asymmetry

Punetha, Nirmal; Karnatak, Rajat; Prasad, Awadhesh; Kurths, Jürgen; Ramaswamy, Ramakrishna

doi:10.1103/physreve.85.046204

Cited by 19 publications

(17 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For asymmetric time-delays, even in the case of two coupled oscillators, the phase difference can be different from π [67]. Such different phase relations have been seen in experiments with asymmetric coupling [106] and time-delay [67] as well as in in relay-coupled nonlinear oscillators [79].…”

Section: The Phase-flipmentioning

confidence: 83%

“…Furthermore, when there are more than two coupled oscillators, the phase-difference is not necessarily π, but can depends upon the specifics of the system as well as on the coupling topology of the network [105]. For asymmetric time-delays, even in the case of two coupled oscillators, the phase difference can be different from π [67]. Such different phase relations have been seen in experiments with asymmetric coupling [106] and time-delay [67] as well as in in relay-coupled nonlinear oscillators [79].…”

Section: The Phase-flipmentioning

confidence: 99%

“…2.7). Mixed interaction schema, with instantaneous interactions in one system and time-delay in the other [65] or unequal time-delays in different directions (to model spatial heterogeneity [66,67] and one-way ring time-delay [37] have been studied in recent works.…”

Section: Delay Interactionmentioning

confidence: 99%

“…[26,27,28,70,67] in a variety of systems, as well as in different dynamical regimes. Furthermore, when there are more than two coupled oscillators, the phase-difference is not necessarily π, but can depends upon the specifics of the system as well as on the coupling topology of the network [105].…”

Section: The Phase-flipmentioning

confidence: 99%

See 3 more Smart Citations

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

Self Cite

View full text Add to dashboard Cite

When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

show abstract

Section: The Phase-flipmentioning

confidence: 83%

Section: The Phase-flipmentioning

confidence: 99%

Section: Delay Interactionmentioning

confidence: 99%

Section: The Phase-flipmentioning

confidence: 99%

See 2 more Smart Citations

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…60 It must be emphasized that most of them enlarge the parameter space where death occurs, as compared with the original delay connection. The consensus problems in networked multi-agent systems have been widely investigated in the field of control theory.…”

Section: Discussionmentioning

confidence: 99%

Design of time-delayed connection parameters for inducing amplitude death in high-dimensional oscillator networks

Sugitani

Konishi

et al. 2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

The present paper studies time-delayed-connection induced amplitude death in high-dimensional oscillator networks. We provide two procedures for design of a coupling strength and a transmission delay: these procedures do not depend on the topology of oscillator networks (i.e., network structure and number of oscillators). A graphical procedure based on the Nyquist criterion is proposed and then is numerically confirmed for the case of five-dimensional oscillators, called generalized Rössler oscillators, which have two pairs of complex conjugate unstable roots. In addition, for the case of high-dimensional oscillators having two unstable roots, the procedure can be systematically carried out using only a simple algebraic calculation. This systematic procedure is numerically confirmed for the case of three-dimensional oscillators, called Moore-Spiegel oscillators, which have two positive real unstable roots.

show abstract

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

Nag

Poria

2016

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

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.

show abstract

Frequency discontinuity and amplitude death with time-delay asymmetry

Cited by 19 publications

References 30 publications

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Design of time-delayed connection parameters for inducing amplitude death in high-dimensional oscillator networks

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

Contact Info

Product

Resources

About