Oscillatory Global Output Synchronization of Nonidentical Nonlinear Systems

Ahmed, Hafiz; Ushirobira, Rosane; Efimov, Denis; Wang, Yongqiang

doi:10.1016/j.ifacol.2017.08.557

Cited by 4 publications

(2 citation statements)

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“…Initially, BO was used to analyze robust synchronization [37]. Later, the nonidentical BO-induced global synchronization was reported [38]. It is further proved that the observed global synchronization has applications in power-grid synchronization and renewable energy sources [39].…”

Section: Introductionmentioning

confidence: 95%

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Collective Dynamical Behaviors of Nonlocally Coupled Brockett Oscillators

Ramadoss¹,

Premraj

Rajagopal

et al. 2023

Mathematical Problems in Engineering

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In this study, we consider a network of nonlocally coupled Brockett oscillators (BOs) with attractive and repulsive (AR) couplings to illustrate the existence of diverse collective dynamical behaviors, whereas previous studies solely concentrated on synchronization. In the absence of coupling, the individual BO oscillator shows stable periodic oscillations (POs) or stable steady state (SS) depending on the critical values of the parameters. We first begin by examining the collective dynamics by setting the critical value of the parameters at the active (PO) region. A diverge collective dynamical states are manifested for a fixed nonlocal coupling range with rising coupling magnitude. Notably, the lower coupling strength exhibits two distinct dynamical patterns at lower and higher transients. At lesser transients, for example, transient dynamics of desynchronization, chimera, and traveling wave states are observed. At larger time periods, the transient dynamics disappear with the emergence of a synchronized state. Increasing the coupling strength results in a unique state of traveling wave or synchronized state for smaller and larger time periods depending on the coupling strength. Increasing the coupling strength further gives rise to clustering behaviors. Importantly, the considered system attains cluster oscillation death (COD) through a cluster oscillatory state (COS). Finally, there exists a chimera death at a larger coupling strength. The observed dynamical transitions are further demonstrated through the two-parameter analysis by setting different critical thresholds.

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Section: Introductionmentioning

confidence: 95%

“…To illustrate the collective dynamical states, we consider a general mathematical model of a Brockett oscillator (BO). Originally, the Brockett oscillator was introduced by R. Brockett in 2013, to study the global synchronization [36][37][38]. Following that, the majority of earlier work on BO focused completely on synchronization behaviors.…”

Section: The Modelmentioning

confidence: 99%