Design of easily synchronizable oscillator networks using the Monte Carlo optimization method

Abstract

Starting with an initial random network of oscillators with a heterogeneous frequency distribution, its autonomous synchronization ability can be largely improved by appropriately rewiring the links between the elements. Ensembles of synchronization-optimized networks with different connectivities are generated and their statistical properties are studied.

Heterogeneity induces emergent functional networks for synchronization

“…To avoid the effect of the biased sampling, we deterministically select the natural frequencies of the oscillators, similarly to [11], as the N -tuple satisfying the constraints:…”

Autonomous learning by simple dynamical systems with delayed feedback

“…Previously, similar problems were treated by using a stochastic Monte Carlo algorithm with replica exchange [15] (the design of networks of identical phase oscillators with maximal synchronization in the presence of noise has also been considered [16]). Now we want to show how to construct an autonomous dynamical system that would include as its subsystem a network of phase oscillators and independently evolve to a state with a desired degree of synchronization.…”

“…However, rational design rapidly becomes difficult when the size of a system is increased and a complex combinatorial optimization problem is approached. Combinatorial optimization methods, such as stochastic Metropolis algorithms and simulated annealing, have been used in systems engineering problems [7][8][9][10][11][12][13][14][15][16]. Thus, analogs of biological signal transduction networks [7][8][9][10] and model oscillatory genetic networks with prescribed output patterns or oscillation periods [11,12] could be constructed.…”

“…Model genetic networks, which could generate definite stationary expression patterns and thus imitate processes relevant for biological morphogenesis [13] or to produce required temporal responses [14], were developed and investigated. Stochastic Metropolis algorithms with replica exchange were employed to design networks of coupled phase oscillators that exhibit high synchronization despite heterogeneities or noise [15,16].…”

On Synchronization of Pinning-Controlled Networks with Reducible and Asymmetric Coupling Matrix

“…By using the technique of pinning only a limited subset of the whole network, [17] showed that the complex network with coupled identical oscillators could be driven onto some desired common reference trajectory. Nowadays, more and more attentions are being paid to the optimization problems of pinning schemes [18][19][20][21]. For instance, the crucial problem that how to select an optimal combination between the number of pinned nodes and the feedback control gain is studied in [19].…”