Amplitude death and resurgence of oscillation in networks of mobile oscillators

Abstract

The phenomenon of amplitude death has been explored using a variety of different coupling strategies in the last two decades. In most of the work, the basic coupling arrangement is considered to be static over time, although many realistic systems exhibit significant changes in the interaction pattern as time varies. In this article, we study the emergence of amplitude death in a dynamical network composed of time-varying interaction amidst a collection of random walkers in a finite region of three dimensional space. We consider an oscillator for each walker and demonstrate that depending upon the network parameters and hence the interaction between them, global oscillation in the network gets suppressed. In this framework, vision range of each oscillator decides the number of oscillators with which it interacts. In addition, with the use of an appropriate feedback parameter in the coupling strategy, we articulate how the suppressed oscillation can be resurrected in the systems' parameter space. The phenomenon of amplitude death and the resurgence of oscillation is investigated taking limit cycle and chaotic oscillators for broad ranges of parameters, like interaction strength k between the entities, vision range r and the speed of movement v.

Enhancing synchrony in multiplex network due to rewiring frequency

“…Since most of the networks are supported with some internal dynamical processes, the study of the combined effect of the network's structure and the dynamical property has great importance in several disciplines. The influence of these two different properties in dynamical networks lead to the discovery of various interesting collective phenomena [6,7]. Among them, one pioneering explorations are synchronization properties [8,9] of coupled network and these phenomena have been mostly studied in the last few decades for its immense applicability in various physical [10] and engineered systems [11].…”

Chimera dynamics in nonlocally coupled moving phase oscillators

“…In the past few years, the interest in the collective dynamics in coupled oscillators has grown rapidly when oscillators may move in space. Different dynamical behaviors have been investigated, such as amplitude death and resurgence of oscillation [38], mobilityenhanced signal response [39], and synchronization [40][41][42]. It has been shown that synchronization time may depend non-monotonically on the mobility of oscillators and the mechanism of driving synchronization are different for different dynamical regimes [43][44][45].…”

Dynamic interaction induced explosive death

“…p-1 arXiv:2101.09262v1 [nlin.AO] 19 Jan 2021 Earlier, Majhi et al [39] reported the emergence of death state in a temporal network of mobile oscillators. But, the focus of our letter is completely different from that Ref.…”

“…This kind of discontinuous transition from the oscillatory state to the death state using dynamic interaction is reported here for the first time to the best of our knowledge. Moreover in case of mobile agents' network [39,43,44], although the mobility of mobile agents affects the collective dynamics of the system, but the states of those oscillators situated on the top of those agents usually do not influence the agents' mobility. To get rid of this unidirectional affair, a dynamic coupling scheme [27] is implemented here, where the mean state of all oscillators decides whether the interaction among those oscillators will appear or not.…”