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This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…
This article studies the rotational dynamics of three identical coupled pendulums. There exist two parameter areas where the in-phase rotational motion is unstable and out-of-phase rotations are realized. Asymptotic theory is developed that…
We consider the rotational dynamics in an ensemble of globally coupled identical pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of…
This study explores a method to characterize temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the…
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…
Intermittent synchronization is observed in a variety of different experimental settings in physics and beyond and is an established research topic in nonlinear dynamics. When coupled oscillators exhibit relatively weak, intermittent…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a…
In this note I survey the extensive literature on the dynamics of large series arrays of identical current biased Josephson junctions coupled through various shared loads. The equations describing the dynamics are invariant under…
In this work, we investigate the synchronization in oscillators with conjugate coupling in which oscillators interact via dissimilar variables. The synchronous dynamics and its stability are investigated theoretically and numerically. We…
The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of…
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
We investigated the locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in the coupling…
We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…