Spatial splay states in coupled map lattices and Josephson junction arrays

Singha, Joydeep; Tchuyang, Valerie; Louodop, Patrick; Tchitnga, Robert; Cerdeira, Hilda A.; Gupte, Neelima

doi:10.29195/iascs.01.01.0018

Cited by 2 publications

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“…2(e) which represents the synchronization in the first layer and a coherent oblique sliding in the second layer. By computing the phase difference between consecutive oscillators (here consecutive refers to the indices of the oscillators) we verified that the phase distance between oscillators of consecutive index in the slave layer is constant, therefore the second layer presents indeed a phenomenon of splay 37,38 . In Fig.…”

Section: A Dynamics Of Different Layersmentioning

confidence: 71%

Dynamics of multilayer networks with amplification

Njougouo

Camargo

Louodop

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study the dynamics of a multilayer network of chaotic oscillators subject to an amplification. Previous studies have proven that multilayer networks present phenomena such as synchronization, cluster and chimera states. Here we consider a network with two layers of Rössler chaotic oscillators as well as applications to multilayer networks of chaotic jerk and Liénard oscillators. Intra-layer coupling is considered to be all to all in the case of Rössler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Liénard, the inter-layer coupling is unidirectional in all these three cases. The second layer has an amplification coefficient. An in-depth study on the case of a network of Rössler oscillators using master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster and phase synchronization with amplification. For the case of Rössler oscillators, we note that there are also certain values of coupling parameters and amplification where the synchronization doesn't exist or the synchronization can exist but without amplification. Using other systems with different topologies, we obtain some interesting results such as chimera state with amplification, cluster state with amplification and complete synchronization with amplification.Research on multilayer networks has attracted a lot of attention in recent years in many areas of physics, engeneering, social sciences etc 1-6 . Some emergent behaviors in such systems due to interaction among the dynamical units reveal a variety of interesting phenomena, such as synchronization 1,7,8 , cluster formation 9 , explosive synchronization 10 , explosive desynchronization 11 , chimera 12-16 etc. Among these, synchronization and chimeras are the most widely studied. The notion of amplification is very important in science and technology. This work presents an investigation of different phenomena such as complete synchronization, cluster formation, phase synchronization and chimera states in a network with amplification. For an extended study we present three cases with three different topologies.

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Section: A Dynamics Of Different Layersmentioning

confidence: 71%

Dynamics of multilayer networks with amplification

Njougouo

Camargo

Louodop

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…However, none of the splay states observed show hyperchaotic behaviour. One application context where such low values of K can be realised is that of coupled Josephson junction arrays with high values of capacitance 56 .…”

Section: Discussionmentioning

confidence: 99%

Chimera states in globally coupled sine circle map lattices: Spatiotemporal intermittency and hyperchaos

Singha

Gupte

2020

Physics Letters A

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We study the existence of chimera states, i.e. mixed states, in a globally coupled sine circle map lattice, with different strengths of inter-group and intra-group coupling. We find that at specific values of the parameters of the CML, a completely random initial condition evolves to chimera states, having a phase synchronised and a phase desynchronised group, where the space time variation of the phases of the maps in the desynchronised group shows structures similar to spatiotemporally intermittent regions. Using the complex order parameter we obtain a phase diagram that identifies the region in the parameter space which supports chimera states of this type, as well as other types of phase configurations such as globally phase synchronised states, two phase clustered states and fully phase desynchronised states. We estimate the volume of the basin of attraction of each kind of solution. The STI chimera region is studied in further detail via numerical and analytic stability analysis, and the Lyapunov spectrum is calculated. This state is identified to be hyperchaotic as the two largest Lyapunov exponents are found to be positive. The distributions of laminar and burst lengths in the incoherent region of the chimera show exponential behaviour. The average fraction of laminar/burst sites is identified to be the important quantity which governs the dynamics of the chimera. After an initial transient, these settle to steady values which can be used to reproduce the phase diagram in the chimera regime.The study of chimera states, i.e. mixed states where synchronised and desynchronised dynamics coexist, has been at the forefront of studies in nonlinear dynamics involving both theoretical and experimental systems. A variety of classes of chimera states, i.e. states which contain coexisting domains of distinct kinds of spatiotemporal behaviour can be seen. These include multi-headed chimera states, travelling chimera states, amplitude chimera states, twisted chimera states etc, and have been seen in coupled oscillator models such as the Kuramoto model,coupled Ginzburg-Landau oscillators and other systems. Here, we investigate chimera and other states in a coupled sine circle map lattice which is a discrete version of coupled oscillator systems. The CML consists of two populations of globally coupled identical sine circle maps with distinct values for the intergroup and intragroup coupling. We observe spatiotemporally intermittent chimeras, i.e. states which consist of a synchronised subgroup, and a state where coherent (phase synchronised) and incoherent (phase incoherent) domains co-exist, at low values of the nonlinearity map parameter. Such STI chimeras have been observed earlier in coupled oscillators models such as Stuart-Landau oscillators, Ginzburg-Landau oscillators, coupled optical resonators, chemical reactions etc. We analyse the STI chimera seen in the CML system by plotting the phase diagram of the system using the global order parameter, and identifying the region where STI chimeras can be seen. The basin...

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Spatial splay states in coupled map lattices and Josephson junction arrays

Cited by 2 publications

References 0 publications

Dynamics of multilayer networks with amplification

Dynamics of multilayer networks with amplification

Chimera states in globally coupled sine circle map lattices: Spatiotemporal intermittency and hyperchaos

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