相关论文: Synchronization, chaos, and breakdown of collectiv…
We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over $d$-dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored…
At incident powers much higher than the threshold for filamentation a pulse from a high-power laser generates in the transversal plane a complex structure. It consists of randomly meandering stripes defining connected regions where the…
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
We report a new mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et. al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules…
We study the global existence of solutions reaction-diffusion systems with control of mass on multiple domains. Some of these domains overlap, and as a result, an unknown defined on one subdomain can impact another unknown defined on a…
Coupling a reaction-diffusion equation with ordinary differential equations (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant…
We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
We study the evolution of a localized perturbation in a chemical system with multiple homogeneous steady states, in the presence of stirring by a fluid flow. Two distinct regimes are found as the rate of stirring is varied relative to the…
Turbulent reacting flows confined to ducts are plagued by thermoacoustic instability, a state in which a positive feedback between flow, flame and acoustic perturbations leads to the emergence of catastrophically high-amplitude oscillatory…
We study phase-separating fluid mixtures as they demix in the presence of chemical reactions that maintain them away from thermodynamic equilibrium. We show that in such chemically active emulsions the interplay of chemical reactions, phase…
Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3-D volume-preserving slow-fast systems. We propose a general theory of those…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share…
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…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…