Related papers: Chaotic motion and singularity structures of front…
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…
The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the…
We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to…
Recent studies of biological, chemical, and physical pattern-forming systems have started to go beyond the classic `near onset' and `far from equilibrium' theories for homogeneous systems to include the effects of spatial heterogeneities.…
We study the front propagation in Reaction-Diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
We investigate a two-component reaction-diffusion system with a slow-fast structure and spatially varying coefficients $f_1$ and $f_2$ appearing in the slow equation. Under mild boundedness and regularity conditions on $f_1$ and $f_2$ the…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading…
We prove the existence of chaotic motions in a planar restricted four body problem, establishing that the system is not integrable. The idea of the proof is to verify the hypotheses of a topological forcing theorem. The forcing theorem…
We consider an Allen-Cahn type equation with a bistable nonlinearity associated to a double-well potential whose well-depths can be slightly unbalanced, and where the coefficient of the nonlinear reaction term is very small. Given rather…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…
We study chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions. It has a time-independent Hamiltonian, in contrast to quantum circuits and Brownian models, and is simple at the single-site…
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular…
In this article, we study the FitzHugh-Nagumo $(1,1)$--fast-slow system where the vector fields associated to the slow/fast equations come from the reduction of the Hodgin-Huxley model for the nerve impulse. After deriving dynamical…
Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a…
We examine a 2DOF Hamiltonian system, which arises in study of first-order mean motion resonance in spatial circular restricted three-body problem "star-planet-asteroid", and point out some mechanisms of chaos generation. Phase variables of…
We consider a nonlinear reaction diffusion system of parabolic type known as the monodomain equations, which model the interaction of the electric current in a cell. Together with the FitzHugh-Nagumo model for the nonlinearity they…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…