Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps

Semenova, Nadezhda; Вадивасова, Т. Е.; Анищенко, В. С.

doi:10.1140/epjst/e2018-800035-y

Cited by 34 publications

(13 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We cannot designate the chimera patterns as strong chimera (Zhang and Motter, 2021). However, some recent reports consider this latter chimera pattern as a solitary state (Jaros et al, 2018;Semenova et al, 2018;Rybalova et al, 2021) since a single oscillator behaves differently, in the dynamical sense, from the other two coherent oscillators.…”

Section: Discussionmentioning

confidence: 97%

Smallest Chimeras Under Repulsive Interactions

Saha¹,

Dana²

2021

Front. Netw. Physiol.

View full text Add to dashboard Cite

We present an exemplary system of three identical oscillators in a ring interacting repulsively to show up chimera patterns. The dynamics of individual oscillators is governed by the superconducting Josephson junction. Surprisingly, the repulsive interactions can only establish a symmetry of complete synchrony in the ring, which is broken with increasing repulsive interactions when the junctions pass through serials of asynchronous states (periodic and chaotic) but finally emerge into chimera states. The chimera pattern first appears in chaotic rotational motion of the three junctions when two junctions evolve coherently, while the third junction is incoherent. For larger repulsive coupling, the junctions evolve into another chimera pattern in a periodic state when two junctions remain coherent in rotational motion and one junction transits to incoherent librational motion. This chimera pattern is sensitive to initial conditions in the sense that the chimera state flips to another pattern when two junctions switch to coherent librational motion and the third junction remains in rotational motion, but incoherent. The chimera patterns are detected by using partial and global error functions of the junctions, while the librational and rotational motions are identified by a libration index. All the collective states, complete synchrony, desynchronization, and two chimera patterns are delineated in a parameter plane of the ring of junctions, where the boundaries of complete synchrony are demarcated by using the master stability function.

show abstract

Section: Discussionmentioning

confidence: 97%

Smallest Chimeras Under Repulsive Interactions

Saha¹,

Dana²

2021

Front. Netw. Physiol.

View full text Add to dashboard Cite

show abstract

“…During the transition, more and more solitary oscillators appear, growing almost linearly with the decrease in the coupling strength. This is the result of an increase of the size of the basin of attraction of the solitary set with a decrease in the coupling, as more random initial conditions lie in this basin [52]. To also induce solitary states in maps with nonhyperbolic attractors, a multiplicative noise can be added to the coupling constant, thus also showing the existence of the solitary state in a noisy system [53].…”

Section: Weakly Coupled Oscillators-kuramoto Modelmentioning

confidence: 99%

Using phase dynamics to study partial synchrony: three examples

Teichmann

2021

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed.

show abstract

“…The surprising aspect of this phenomenon is that these states were detected in systems of identical oscillators coupled in a symmetric ring topology with a symmetric interaction function, and they coexist with a stable completely synchronized state. The last a) Electronic mail: zergon@gmx.net decade has seen an increasing interest in phase and amplitude chimeras both in time-continuous systems [14][15][16][17][18][19][20][21][22] and in timediscrete maps [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] . It has been shown that they are not limited to phase oscillators, but can be found for a large variety of different dynamics including neural systems [42][43][44][45][46][47][48] .…”

Section: Introductionmentioning

confidence: 99%

Synchronization scenarios in three-layer networks with a hub

Sawicki,

Koulen,

Schöll

2021

Preprint

View full text Add to dashboard Cite

Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps

Cited by 34 publications

References 23 publications

Smallest Chimeras Under Repulsive Interactions

Smallest Chimeras Under Repulsive Interactions

Using phase dynamics to study partial synchrony: three examples

Synchronization scenarios in three-layer networks with a hub

Contact Info

Product

Resources

About