Emergence of chimeras through induced multistability

Ujjwal, Sangeeta Rani; Punetha, Nirmal; Prasad, Awadhesh; Ramaswamy, Ramakrishna

doi:10.1103/physreve.95.032203

Cited by 19 publications

(16 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3. It should be noted that these attractors are similar to those reported earlier by Ujjwal et al [19], where chimera states in an ensemble of globally coupled Lorenz oscillators were studied. It was proposed that the attractors A 1 and A 2 appear as a result of change in the effective parameters of the system and the effective modulation of symmetric fixed points due to coupling between the oscillators.…”

Section: Coupled Lorenz Systems Near the Hopf Bifurcationsupporting

confidence: 87%

“…Our motivation arises in part from the observation [19] that coupling dynamical systems effectively alters the values of the parameters governing the flows. In addition the coupling can affect the stability of the coupled dynamics and therefore it becomes important to examine the dynamics of coupled systems in the neighbourhood of bifurcations since here fundamentally new phenomena can arise.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling

et al. 2017

View full text Add to dashboard Cite

We investigate the dynamics of coupled identical chaotic Lorenz oscillators just above the subcritical Hopf bifurcation. In the absence of coupling, the motion is on a strange chaotic attractor and the fixed points of the system are all unstable. With the coupling, the unstable fixed points are converted into chaotic attractors, and the system can exhibit a multiplicity of coexisting attractors. Depending on the strength of the coupling, the motion of the individual oscillators can be synchronized (both in and out of phase) or desynchronized and in addition there can be mixed phases. We find that the basins have a complex structure: the state that is asymptotically reached shows extreme sensitivity to initial conditions. The basins of attraction of these different states are characterized using a variety of measures and depending on the strength of the coupling, they are intermingled or quasiriddled.

show abstract

Section: Coupled Lorenz Systems Near the Hopf Bifurcationsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Multistability induced by the coupling can also appear in continuous time coupled oscillators 44 . Our results suggest that asymmetric cluster and chimera states may be induced by an external constant uniform field acting on an ensemble of chaotic oscillators.…”

Section: Discussionmentioning

confidence: 99%

Asymmetric cluster and chimera dynamics in globally coupled systems

Cano

Cosenza

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We investigate the emergence of chimera and cluster states possessing asymmetric dynamics in globally coupled systems, where the trajectories of oscillators belonging to different subpopulations exhibit different dynamical properties. In an asymmetric chimera state, the trajectory of an element in the synchronized subset is stationary or periodic, while that of an oscillator in the desynchronized subset is chaotic. In an asymmetric cluster state, the periods of the trajectories of elements belonging to different clusters are different. We consider a network of globally coupled chaotic maps as a simple model for the occurrence of such asymmetric states in spatiotemporal systems. We employ the analogy between a single map subject to a constant drive and the effective local dynamics in the globally coupled map system to elucidate the mechanisms for the emergence of asymmetric chimera and cluster states in the latter system. By obtaining the dynamical responses of the driven map, we establish a condition for the equivalence of the dynamics of the driven map and that of the system of globally coupled maps. This condition is applied to predict parameter values and subset partitions for the formation of asymmetric cluster and chimera states in the globally coupled system.Recently a fascinating phenomenon occurring in networks of coupled identical oscillators has attracted much attention from researchers in various fields: chimera states. A chimera state consists of the simultaneous coexistence of subsets of oscillators with synchronous (coherent) and asynchronous (incoherent) dynamics. This behavior represents a state of broken synchronization symmetry and has been studied theoretically and experimentally in different contexts and also with a variety of coupling schemes. In systems with global interactions, chimera states are related to the formation of clusters, where the system segregates into distinguishable subsets of synchronized elements. Here we investigate the emergence of chimera states possessing asymmetric dynamics, in the sense that the dynamical evolution of oscillators belonging to the synchronized or the desynchronized subset are different: the trajectory shared by the oscillators in the synchronized subset is stationary, while that of an oscillator in the desynchronized subset is chaotic. Similarly, we investigate asymmetric cluster states, where the periods of the orbits of oscillators belonging to different clusters are different. In particular, the coexistence of synchronized and desynchronized subsets possessing asymmetric dynamics represents a further breaking of the synchronization symmetry in a system of coupled identical oscillators.

show abstract

“…These states were also studied for a globally coupled network of semiconductor lasers with delayed optical feedback [20]. Recently, it has been shown that the chimera states may emerge as a result of induced multistability due to the couplings that bring the system parameters in a multistable regime [6]. The coupling effectively changes the parameter of the system leading to multistable dynamics and finally the creation of chimera states.…”

Section: Introductionmentioning

confidence: 99%

“…Earlier studies have shown that coupled oscillators should have weak and nonlocal coupling to show chimera states. At other instances it was argued that for globally coupled oscillators chimera states can occur as a result of multistability [5,6]. On changing the coupling parameter the transition to various collective states can be achieved depending upon initial conditions.…”

mentioning

confidence: 99%

Occurrence and stability of chimera states in multivariable coupled flows

Khatun,

Jafri

2019

Preprint

View full text Add to dashboard Cite

Study of collective phenomenon in populations of coupled oscillators are a subject of intense exploration in physical, biological, neuronal and social systems. Here we propose a scheme for the creation of chimera states, namely the coexistence of distinct dynamical behaviors in an ensemble of multivariable coupled oscillatory systems and a novel scheme to study their stability. We target bifurcation parameters that can be tuned such that out of the two coupling parameters one pushes the system to synchrony while the other one takes it to the desynchronized state. The competition between these states result in a situation that a certain fraction of oscillators are synchronized while others are desynchronized thereby producing a mixed chimera state. Further changes in couplings can result in the desired form of the state which could be completely synchronized or desynchronized. Using the model example of coupled Rössler systems we show that their basin of attraction are either riddled or intertwined. We use Strength of incoherence and Master Stability function (MSF) as the order parameters to verify the stability of chimera states. MSF for different attractors are found to possess both negative and positive values indicating the coexistence of stable synchronized dynamics with desynchronized state.

show abstract

Emergence of chimeras through induced multistability

Cited by 19 publications

References 41 publications

Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling

Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling

Asymmetric cluster and chimera dynamics in globally coupled systems

Occurrence and stability of chimera states in multivariable coupled flows

Contact Info

Product

Resources

About