Related papers: Bifurcation analysis and structural stability of s…
Hydrodynamic instabilities often cause spatio-temporal pattern formations and transitions between them. We investigate a model experimental system, a density oscillator, where the bifurcation from a resting state to an oscillatory state is…
We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis,…
Study of collective phenomenon in populations of coupled oscillators are a subject of intense exploration in physical, biological, neuronal and social systems. Here we propose a scheme for the creation of chimera states, namely the…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
Self-organized criticality is a well-established phenomenon, where a system dynamically tunes its structure to operate on the verge of a phase transition. Here, we show that the dynamics inside the self-organized critical state are…
We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…
We investigate a model of globally coupled conservative oscillators. Two different algebraic potentials are considered that display in the canonical ensemble either a second ($\phi^{4}$) or both a second and a first order phase transition…
A coupled-phase oscillator model where each oscillator has an angular velocity that varies due to the interaction with other oscillators is studied. This model is proposed to deepen the understanding of the relationship between the…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a…
Clustering bifurcations are investigated by considering models of globally coupled map lattices. Typical classes of clustering bifurcations are revealed. The clustering bifurcation thresholds of the coupled system are closely related to the…
Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our…
In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…
We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…