Synchronization extends the life time of the desired behavior of globally coupled systems

Abstract

Synchronization occurs widely in natural and technological world, but it has not been widely used to extend the life time of the desirable behavior of the coupled systems. Here we consider the globally coupled system consisting of n units and show that the initial synchronous state extends the lifetime of desired behavior of the coupled system in the case when the excitation of one or few units is suddenly (breakdown of energy supply) or gradually (as the effect of aging and fatigue) switched off. We give evidence that for the properly chosen coupling the energy transfer from the excited units allows unexcited units to operate in the desired manner. As proof of concept, we examine the system of coupled externally excited rotating pendula. After the partial excitation switch off the initial complete synchronization of all pendula is replaced by phase synchronization with a constant phase shift between the clusters of excited and unexcited pendula. Our results show that the described extension of the system's life time occurs for the wide range of coupling parameters and is robust to the external perturbations.

Synchronization and Stability of Two Unbalanced Rotors with Fast Antirotation considering Energy Balance

“…Recently, Koluda and Perlikowski derived the synchronization conditions and explained the energy transmission between double pendula via an oscillating beam with energy balance method [13][14][15]. Kapitaniak et al explored synchronous states of slowly rotating pendula considering the oscillating beam moving in a single DOF [16,17]. Pena-Ramírez concerned the synchronized motion of Huygens' model building on the original work of Blekhman [18,19].…”

Chimera-like states generated by large perturbation of synchronous state of coupled metronomes

“…The coexistence of the synchronous state with various chimera-like states raises the question of synchronization survivability under different perturbations which are always present in real-world systems [43,44]. Here we show that the patterns of the chimera-like and solitary states can be observed both in simulations and experiments in the networks of mechanical oscillators after the large perturbation (in which one or a few oscillators have been stopped for the moment) of the synchronous state of the whole network.…”

“…The amount of the dissipative energy is not sufficient to change its frequency and all excited pendula oscillate with the same frequency different from the frequency of unexcited ones. The signal transferred from the unperturbed pendula 9 and 13 (through the coupling to the second nearest neighbors) allows the preservation of synchronization [44]. In the case of figure 4b and c the number of neighboring unexcited pendula is larger (respectively 4 and 6).…”

Synchronization in Coupled Multistable Systems with Hidden Attractors

“…Synchronization of dynamical systems has become a field of intense interest and hence extensive study in the last decades [1][2][3][4][5][6][7][8]. Just the dynamical systems alone have been known to exhibit a wide variety of complex behavior.…”