Related papers: Optimizing mutual synchronization of rhythmic spat…
We present the first report on chaos synchronization between two unidirectionally linearly and nonlinearly coupled systems with multiple time-delays and using the Razumikhin-Lyapunov approach find the existence and stability conditions for…
In this paper we investigate the reaction--diffusion system corresponding to the Newton--Leipnik chaotic system originally developed to model the rigid body motion through linear feedback (LFRBM). We develop a nonlinear synchronization…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…
The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex…
We study the dynamics of a lattice of coupled nonidentical Fitz Hugh-Nagumo system subject to independent external noise. It is shown that these stochastic oscillators can lead to global synchronization behavior {\sl without an external…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the…
A new mathematical model of memristive neural networks described by the partly diffusive reaction-diffusion equations with weak synaptic coupling is proposed and investigated. Under rather general conditions it is proved that there exists…
We study a nonlinear coupled system of partial differential equations arising from thermo--reaction--phase models. The system combines a heat diffusion equation, temperature-dependent chemical reactions of Arrhenius type, and a phase…
We experimentally demonstrate synchronization between two distinct ensembles of cold atoms undergoing steady state superradiance within a single longitudinal and transverse mode of the same optical cavity. The synchronization process is…
We develop a phase reduction method for reaction-diffusion systems with a discrete delay. On the basis of the recent developments in the phase reduction theory for infinite-dimensional systems, we introduce a bilinear form tailored to…
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…
Feedback optimization algorithms compute inputs to a system using real-time output measurements, which helps mitigate the effects of disturbances. However, existing work often models both system dynamics and computations in either discrete…
We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
Synchronization is studied in a spatially-distributed network of weekly-coupled, excitatory neurons of Hodgkin-Huxley type. All neurons are coupled to each other synaptically with a fixed time delay and a coupling strength inversely…