Delay-induced remote synchronization in bipartite networks of phase oscillators

Punetha, Nirmal; Ujjwal, Sangeeta Rani; Atay, Fatihcan M.; Ramaswamy, Ramakrishna

doi:10.1103/physreve.91.022922

Cited by 13 publications

(10 citation statements)

References 38 publications

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“…Equation (30) shows that the number of overlaps m increases linearly with n. As noted above, we have r" = htt/ cd e /". Therefore, the number of coexisting stable synchronized solutions increases essentially linearly with increasing mean delay r and grows unbounded [cf.…”

Section: Multistability Of Synchronized Solutions In Kuramoto Osmentioning

confidence: 87%

Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability

2015

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We study synchronization in bipartite networks of phase oscillators with general nonlinear coupling and distributed time delays. Phase-locked solutions are shown to arise, where the oscillators in each partition are perfectly synchronized among themselves but can have a phase difference with the other partition, with the phase difference necessarily being either zero or π radians. Analytical conditions for the stability of both types of solutions are obtained and solution branches are explicitly calculated, revealing that the network can have several coexisting stable solutions. With increasing value of the mean delay, the system exhibits hysteresis, phase flips, final state sensitivity, and an extreme form of multistability where the numbers of stable in-phase and antiphase synchronous solutions with distinct frequencies grow without bound. The theory is applied to networks of Landau-Stuart and Rössler oscillators and shown to accurately predict both in-phase and antiphase synchronous behavior in appropriate parameter ranges.

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Section: Multistability Of Synchronized Solutions In Kuramoto Osmentioning

confidence: 87%

Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability

2015

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“…Apart from their application to a variety of physical [3,4] and biological [5,6] situations, the robustness of such complexity has attracted considerable recent interest. Earlier studies have suggested that in order to observe chimera states, some degree of nonuniformity is essential [7], and this nonuniformity can arise due to heterogeneities in the coupling [1,[8][9][10], in the topology [11,12], parameters [13][14][15], or by allowing for amplitude variation [16]. It has also been seen that time-delay coupling can cause nonuniformity, although it is possible that chimera states reported in several theoretical studies are long transients [17,18].…”

Section: Introductionmentioning

confidence: 99%

Emergence of chimeras through induced multistability

et al. 2017

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Chimeras, namely coexisting desynchronous and synchronized dynamics, are formed in an ensemble of identically coupled identical chaotic oscillators when the coupling induces multiple stable attractors, and further when the basins of the different attractors are intertwined in a complex manner. When there is coupling-induced multistability, an ensemble of identical chaotic oscillators-with global coupling, or also under the influence of common noise or an external drive (chaotic, periodic, or quasiperiodic)-inevitably exhibits chimeric behavior. Induced multistability in the system leads to the formation of distinct subpopulations, one or more of which support synchronized dynamics, while in others the motion is asynchronous or incoherent. We study the mechanism for the emergence of such chimeric states, and we discuss the generality of our results.

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“…A solution of this type is termed a splay phase and known to occur in a variety of dynamical systems; this is the generalisation of the anti-phase solution that occurs in the bipartite system [21,22]. Apart from these generic solutions, existing for all values of τ , there can be other phase locked solutions as well, and these can be calculated on a case-by-case basis, depending on the number of partitions in the network and the parameters ε and τ .…”

Section: Phase Oscillators On a K−partite Networkmentioning

confidence: 99%

“…Notice that there is a range of values of τ where there is only a single stable state, as well as parameter ranges when there are several stable frequencies [18]. The width of this latter range increases with increasing coupling strength [21].…”

Section: Phase Oscillators On a K−partite Networkmentioning

confidence: 99%

“…Punetha et.al. [21] showed that a discrete time-delay, can lead to remote synchronisation of the oscillators for appropriate frequency mismatch between the partitions. For a general bipartite system of oscillators, the exact stability criteria for in-phase and anti-phase solutions have been obtained [22], and it has been proved that these are indeed the generic solutions.…”

Section: Introductionmentioning

confidence: 99%

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Phase-locking in $k$-partite networks of delay-coupled oscillators

Singha,

Ramaswamy

2021

Preprint

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We examine the dynamics of an ensemble of phase oscillators that are divided in k sets, with timedelayed coupling interactions only between oscillators in different sets or partitions. The network of interactions thus form a k−partite graph. We observe a variety of phase-locked states that include, in addition to the in-phase fully synchronized solution, a variety of splay cluster solutions; all oscillators within a partition are synchronised and the phase differences between oscillators in different partitions are multiples of 2π/k. Such solutions exist independent of the delay and we determine the generalised stability criteria for the existence of these phase-locked solutions for the k−partite system. With increase in time-delay, there is an increase in multistability: the above generic solutions coexist with a number of other partially synchronized solutions. We apply the Ott-Antonsen ansatz for the special case of a symmetric k−partite graph to obtain a single time-delayed differential equation for the attracting synchronization manifold. The agreement with numerical results for the specific case of oscillators on a tripartite lattice (the k = 3 case) is excellent.

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Delay-induced remote synchronization in bipartite networks of phase oscillators

Cited by 13 publications

References 38 publications

Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability

Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability

Emergence of chimeras through induced multistability

Phase-locking in $k$-partite networks of delay-coupled oscillators

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