Spatial splay states and splay chimera states in coupled map lattices

Singha, Joydeep; Gupte, Neelima

doi:10.1103/physreve.94.052204

Cited by 13 publications

(18 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, we study the existence of chimera states in a coupled map lattice which is a discrete analog of coupled phase oscillator system where both space and time are considered to be discrete. The chimera phase state as well as other other mixed states were reported in specific systems of coupled map lattices in both theoretical 29,30 models and experimental systems 31,32 . The CML, used here, is of the form used in Refs.…”

Section: Introductionmentioning

confidence: 86%

“…The CML, used here, is of the form used in Refs. 29,30 and consists of two populations of globally coupled identical sine circle maps where the strength of the coupling within each population and that between the maps belonging to distinct populations take different values. Oscillator models with two species of identical dynamical units, leading to chimera states have been explored earlier in refs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Singha

Gupte

2020

Physics Letters A

Self Cite

View full text Add to dashboard Cite

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...

show abstract

Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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

Singha

Gupte

2020

Physics Letters A

Self Cite

View full text Add to dashboard Cite

show abstract

“…22 Nayak and Gupte 45 reported on chimera states in two populations of sine-circle maps. The first experimental observation of chimeras in electro-optical coupled map lattices in one and two dimensions was provided by Hagerstrom et al 24 Apart from coupled logistic maps, 22,23,[27][28][29][30][37][38][39][41][42][43][44] chimera states were illustrated for coupled Henon maps, 26,[32][33][34]36 sinecircle maps, 45,46 sine-squared maps, 35,44 cosine maps, 24 piecewise linear and logistic maps, 25 and cubic maps. 31,39,40 They were found for ring networks with nonlocal coupling, [22][23][24][25][26][28][29][30][31][32][33][34][35][36]39,[41][42]…”

Section: Articlementioning

confidence: 99%

Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics

Andrzejak

Ruzzene

Schöll

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We numerically study a network of two identical populations of identical real-valued quadratic maps. Upon variation of the coupling strengths within and across populations, the network exhibits a rich variety of distinct dynamics. The maps in individual populations can be synchronized or desynchronized. Their temporal evolution can be periodic or aperiodic. Furthermore, one can find blends of synchronized with desynchronized states and periodic with aperiodic motions. We show symmetric patterns for which both populations have the same type of dynamics as well as chimera states of a broken symmetry. The network can furthermore show multistability by settling to distinct dynamics for different realizations of random initial conditions or by switching intermittently between distinct dynamics for the same realization. We conclude that our system of two populations of a particularly simple map is the most simple system that can show this highly diverse and complex behavior, which includes but is not limited to chimera states. As an outlook to future studies, we explore the stability of two populations of quadratic maps with a complex-valued control parameter. We show that bounded and diverging dynamics are separated by fractal boundaries in the complex plane of this control parameter.

show abstract

“…Finally, it should be noted that in case of global coupling other kinds of solutions to the laser equations (4-6) can be found, such as splay states and chimera states (i.e. coexisting synchronous and desynchronous oscillatory behavior) 78,91,92 . Recently, chimera states in nearest-neighbor coupling semiconductor lasers with Hermitian coupling and frequency detuning have been studied in Ref.…”

Section: (C)mentioning

confidence: 99%

Invited Article: Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling

Longhi

Feng

2018

APL Photonics

View full text Add to dashboard Cite

Arrays of coupled semiconductor lasers are systems possessing complex dynamical behavior that are of major interest in photonics and laser science. Dynamical instabilities, arising from supermode competition and slow carrier dynamics, are known to prevent stable phase locking in a wide range of parameter space, requiring special methods to realize stable laser operation. Inspired by recent concepts of parity-time (PT ) and non-Hermitian photonics, in this work we consider non-Hermitian coupling engineering in laser arrays in a ring geometry and show, both analytically and numerically, that non-Hermitian coupling can help to mitigate the onset of dynamical laser instabilities. In particular, we consider in details two kinds of nearest-neighbor non-Hermitian couplings: symmetric but complex mode coupling (type-I non-Hermitian coupling) and asymmetric mode coupling (type-II non-Hermitian coupling). Suppression of dynamical instabilities can be realized in both coupling schemes, resulting in stable phase-locking laser emission with the lasers emitting in phase (for type-I coupling) or with π/2 phase gradient (for type-II coupling), resulting in a vortex far-field beam. In type-II non-Hermitian coupling, chirality induced by asymmetric mode coupling enables laser phase locking even in presence of moderate disorder in the resonance frequencies of the lasers. arXiv:1802.05439v2 [physics.optics]

show abstract

Spatial splay states and splay chimera states in coupled map lattices

Cited by 13 publications

References 26 publications

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

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

Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics

Invited Article: Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling

Contact Info

Product

Resources

About