Chimera states in three dimensions

Maistrenko, Yuri; Sudakov, Oleksandr; Osiv, Oleksiy; Maistrenko, Volodymyr

doi:10.1088/1367-2630/17/7/073037

Cited by 121 publications

(82 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Coupling strength is characterized by the parameter σ. For multidimensional ensembles a sphere with a specified radius R is often considered instead of the square [41,50,32]. In this case R is normalized by the total number of elements and is called coupling radius.…”

Section: Modelmentioning

confidence: 99%

“…Elements from the coherent cluster act in synchrony, while the oscillators from the incoherent cluster are not correlated and form a domain of spatial chaos with fixed borders. Chimeras were found in ensembles of phase oscillators [27,28,29,30,31,32], periodic self-sustained oscillators [33,34,35,36,37,38,39], chaotic oscillators and chaotic return maps [40,41,42,43,44,45,46], networks of oscillatory elements containing blocks of excitable elements [47] or only excitable units [48]. Chimera structures were obtained not only in numerical simulations but also in experiments [49,50,51,52,53,54].…”

Section: Introductionmentioning

confidence: 99%

“…each element is coupled to a certain number of its nearest neighbors. There are also works on 2D-lattice [41,50,54] and 3D-lattice [32]. The chimeras in the form of spiral waves [68] have been observed in the model of 2D medium with phase dynamics of elements.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Double-well chimeras in 2D lattice of chaotic bistable elements

Shepelev

Bukh

Вадивасова

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

We investigate spatio-temporal dynamics of a 2D ensemble of nonlocally coupled chaotic cubic maps in a bistability regime. In particular, we perform a detailed study on the transition "coherence -incoherence" for varying coupling strength for a fixed interaction radius. For the 2D ensemble we show the appearance of amplitude and phase chimera states previously reported for 1D ensembles of nonlocally coupled chaotic systems. Moreover, we uncover a novel type of chimera state, double-well chimera, which occurs due to the interplay of the bistability of the local dynamics and the 2D ensemble structure. Additionally, we find double-well chimera behaviour for steady states which we call double-well chimera death. A distinguishing feature of chimera patterns observed in the lattice is that they mainly combine clusters of different chimera

show abstract

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Double-well chimeras in 2D lattice of chaotic bistable elements

Shepelev

Bukh

Вадивасова

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

show abstract

“…The elements of such ensembles can be oscillators with significantly different behavior, e.g. phase oscillators [2,3,4,6,7], self-sustained oscillatory systems with periodic dynamics [5,8,9,10,11], chaotic oscillators and chaotic return maps [12,13,14,15,16]. The FitzHugh-Nagumo (FHN) oscillator is not an exception in this respect.…”

Section: Introductionmentioning

confidence: 99%

New type of chimera structures in a ring of bistable FitzHugh–Nagumo oscillators with nonlocal interaction

et al. 2017

View full text Add to dashboard Cite

show abstract

“…The existence of chimera states has been experimentally confirmed in diverse systems such as coupled maps [10], chemical oscillators [11,12], and mechanical pendulums [13]. In two-dimensional systems, chimera states usually take the form of spiral waves [17][18][19][20][21][22][23]. These so-called spiral wave chimeras exhibit phase-locked oscillators in the spiral arm but a phase-randomized spiral core [17].…”

mentioning

confidence: 99%

Spiral wave chimeras in locally coupled oscillator systems

Dierckx

2016

Phys. Rev. E

View full text Add to dashboard Cite

The recently discovered chimera state involves the coexistence of synchronized and desynchronized states for a group of identical oscillators. In this work, we show the existence of (inwardly) rotating spiral wave chimeras in the three-component reaction-diffusion systems where each element is locally coupled by diffusion. A transition from spiral waves with the smooth core to spiral wave chimeras is found as we change the local dynamics of the system or as we gradually increase the diffusion coefficient of the activator. Our findings on the spiral wave chimera in the reaction-diffusion systems suggest that spiral chimera states may be found in chemical and biological systems that can be modeled by a large population of oscillators indirectly coupled via a diffusive environment.

show abstract

Chimera states in three dimensions

Cited by 121 publications

References 66 publications

Double-well chimeras in 2D lattice of chaotic bistable elements

Double-well chimeras in 2D lattice of chaotic bistable elements

New type of chimera structures in a ring of bistable FitzHugh–Nagumo oscillators with nonlocal interaction

Spiral wave chimeras in locally coupled oscillator systems

Contact Info

Product

Resources

About