New Approach to Multiplicative Stochastic Processes. I

Simple estimation of synchronization threshold in ensembles of diffusively coupled chaotic systems

“…The above conditions of synchronization stay in agreement with the results obtained earlier by means of other approaches [5,11,16].…”

“…It has been demonstrated that two or more chaotic systems can synchronize by linking them with mutual coupling or with a common signal or signals (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). In the case of identical chaotic systems, i.e., the same set of ordinary different equations (ODEs) and values of the system parameters, complete synchronization can be obtained.…”

“…The first analytical condition for complete synchronization of the sets of symmetrically coupled identical continuous-time dynamical systems has been formulated in [4]. Next this condition has been developed for discretetime systems [5,11]. Many approaches have been applied for describing the synchronization problem for particular coupling configurations as well as for more general cases [3,11,[15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Nonlinear Dynamics of Chaotic and Stochastic Systems

“…Partial frequency-phase synchronization in chains and arrays of quasi-harmonic self-sustained oscillators and phase oscillators manifests itself in the formation of phase and frequency clusters in the presence of basic frequency mismatch [172,173,218,[284][285][286][287]. A large number of publications are devoted to the study of global and partial synchronization, to the formation of clusters of synchronous states and of ordered spatial structures in chains and arrays of identical chaotic self-sustained oscillators and in model chaotic maps [207,282,[288][289][290][291][292][293]. A large number of publications are devoted to the study of global and partial synchronization, to the formation of clusters of synchronous states and of ordered spatial structures in chains and arrays of identical chaotic self-sustained oscillators and in model chaotic maps [207,282,[288][289][290][291][292][293].…”

Bifurcation diagrams in relation to synchronization in chaotic systems

“…The question whether two chaotic systems coupled by some means may be forced to follow the same (or functionally related) paths on the respective attractors did raise interest in the scientific community long ago with the works of Yamada and Fujisaka [1,2], and Afraimovich et al [3] who dealt with coupled chaotic systems. The subject of synchronization was thus brought forth.…”