Synchronization of Multistable Systems

Pisarchik, Alexander N.; Jaimes-Reátegui, R.; García-López, J. H.

doi:10.1142/s0218127408021385

Cited by 23 publications

(27 citation statements)

References 52 publications

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“…A few recent works have focused on synchronization of coupled systems composed of single units that exhibit multi-stable or coexisting behaviors when isolated [29][30][31][32][33][34][35][36][37]; for example, the coupled system composed of two Rössler-like electronic circuits with coexisting chaotic attractors [29][30][31], two coupled Hénon maps with coexisting periodic behaviors [32], two optical bi-stable systems (with coexistence of fixed point and chaos, of fixed point and periodic attractor, and of two periodic attractors) transition from nonsynchronization to complete synchronization (CS) via various complex synchronous states as the coupling strength increases [33]. In addition to these unidirectionally coupled systems, there are investigations on the bidirectionally coupled systems with coexisting behaviors [34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain

Pan

2015

Nonlinear Dyn

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As the value of a control parameter decreases, monostable bursting changes to monostable spiking via the coexistence of spiking and bursting in a Leech neuron model, and the attraction domain of the bursting decreases, while that of the coexisting spiking increases for coexisting behaviors. As the coupling strength increases, the two coupled Leech neurons with the coexisting spiking and bursting manifest transitions from non-synchronization to complete synchronization (CS) through a complex process, which is dependent of the values of the control parameter, cases of configurations (one neuron spiking and the other bursting, both bursting, and both spiking), and the initial values of the two neurons. The transition processes involve various spiking and bursting or chaos synchronization states for the first two cases given here, but contain only spiking patterns for the last case. Corresponding with the attraction domain, the probability of initial values that can lead to bursting patterns of CS decreases, but the probability of initial values that can induce spiking of CS increases for the former two cases, as the control parameter is decreased. This phenomenon can also be interpreted by the structure and volume of the attraction domain with which all initial values can only induce CS of spiking for case 3. The results may improve understanding of the synchronization dynamics of the coupled neurons with coexisting behaviors.

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Section: Introductionmentioning

confidence: 99%

The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain

Pan

2015

Nonlinear Dyn

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show abstract

“…In recent years, the focus on synchronization has been extended from monostable dynamical systems to multi-stable dynamical systems [34][35][36]. Different synchronization (intermittent, phase, anticipated, and period-doubling) states have been observed in two undirectionally coupled identical systems with co-existing chaotic attractors [34,35].…”

Section: Introductionmentioning

confidence: 99%