Ring Of Coupled Oscillators Research Articles

Travelling Waves in the Ring of Coupled Oscillators with Delayed Feedback

We studied travelling waves in N nonlinear differential equations with a delay and large parameter. This system is important because it can be regarded as a phenomenological model of N-coupled neuron-like oscillators with delay. The problem of the existence of travelling-wave-type solutions was reduced to the study of the dynamics of an auxiliary equation with two delays. Using a special asymptotic method for the large parameter we proved that this equation has a relaxation cycle, studied its properties (amplitude, period and asymptotics) and found the sufficient stability conditions. Based on this periodic solution the travelling waves of the initial model were constructed.

Emergence of Self-Organized Dynamical Domains in a Ring of Coupled Population Oscillators

We show that interactions of inherently chaotic oscillators can lead to coexistence of regular oscillatory regimes and chaotic oscillations in the rings of coupled oscillators provided that the level of interaction between the oscillators exceeds a threshold value. The transformation of the initially chaotic dynamics into the regular dynamics in a number of the coupled oscillators is shown to result from suppression of chaos by separation of certain oscillation periods from the continuous spectra, which are characteristic of chaotic oscillations.

Splay States in a Ring of Coupled Oscillators: From Local to Global Coupling

In this work, we study dynamical behavior in a ring of coupled nonlinear oscillators and focus on the stability of homogeneous steady state and splay states by performing linear stability analysis. Different cases from local (nearest-neighbor) coupling to global (all-to-all) coupling by increasing the range of coupling are studied. Some explicit stability results for each possible splay state are analytically obtained. It is valuable to compare their similarities and differences for these different cases. All these results could shed improved light on our understanding of the organization of splay states in coupled oscillators.