Related papers: Bifurcations and Intermittency in Coupled Dissipat…
We prove that steady state bifurcations in finite-dimensional dynamical systems that are symmetric with respect to a monoid representation generically occur along an absolutely indecomposable subrepresentation. This is stated as a…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
In the present work we consider a diatomic granular crystal, consisting of alternating aluminum and steel spheres, where the first sphere is an aluminum one. The combination of dissipation, driving of the boundary, and intrinsic…
A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $\epsilon$. The random fluctuations of the system at the critical point are studied…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
The intermittent route to spatio-temporal complexity is analyzed in a simple model which displays a subcritical bifurcation without hysteresis. A new type of spatio-temporal complexity is found, induced by fronts which "convectively clean"…
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
We explore theoretically the complex dynamics and emergent behaviors of spinning spheres immersed in viscous fluid. The particles are coupled to each-other via the fluid in which they are suspended: each particle disturbs the surrounding…
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems…
We introduce a simple dynamical model of two interacting communities whose elements are subject to stochastic discrete-time updates governed by only bilinear interactions. When the intra- and inter-couplings are cooperative, the two…
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…
Two classical, damped and driven spin oscillators with an isotropic exchange interaction are considered. They represent a nontrivial physical system whose equations of motion are shown to allow for an analytic treatment of local codimension…
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…
We study dynamics of a ring of three unidirectionally coupled double-well Duffing oscillators for three different values of the damping coefficient: fixed dumping, proportional to time, and inversely proportional to time. The dynamics in…
Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors…
Propagation of transition fronts in models of coupled oscillators with non-degenerate on-site potential is usually considered in terms of travelling waves. We show that the system dynamics can be reformulated as an implicit map structure,…