Conditions under which a single oscillator model coupled with Dieterich-Ruina’s rate and state dependent friction exhibits chaotic dynamics is studied. Properties of spring-block models are discussed. The parameter values of the system are explored and the corresponding numerical solutions presented. Bifurcation analysis is performed to determine the bifurcations and stability of stationary sol...

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics of the system. We prove that, in a random regulatory network, initial conditions almost certainly converge to a periodic attractor. We study the subnetworks, ...

It is shown that one can convert a chaotic attractor to any one of a large number of possible attracting time-periodic motions by making only small time-dependent perturbations of an available system parameter. The method utilizes delay coordinate embedding, and so is applicable to experimental situations in which a priori analytical knowledge of the system dynamics is not available. Important ...

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting exam...

Chaotically spiking attractors in semiconductor lasers with optoelectronic feedback have been recently observed to be the result of canard phenomena in three-dimensional phase space (incomplete homoclinic scenarios). Since light-emitting diodes display the same dynamics and are much more easily controllable, we use one of these systems to complete the attractor analysis demonstrating experiment...

The average lifetime (τ(H)) it takes for a randomly started trajectory to land in a small region (H) on a chaotic attractor is studied. τ(H) is an important issue for controlling chaos. We point out that if the region H is visited by a short periodic orbit, the lifetime τ(H) strongly deviates from the inverse of the naturally invariant measure contained within that region (μN (H) −1). We introd...

Controlling chaos has become a challenging topic in nonlinear dynamics. It has been studied in many scientific and engineering fields such as physics, chemistry, electrical circuit, etc., and several extension and applications of the original OGY control method [1] have been reported [2–6]. Chua’s circuit is known as an electrical circuit and having the ability of generating chaos [7]. Recent r...

The finest state-space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation, the stochastic neighborhoods of deterministic periodic orbits can be computed from distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulas for widths of these distributions in ...

In this paper I will investigate the bifurcation and asymptotic behavior of solutions of the Swift-Hohenberg equation and the generalized Swift-Hohenberg equation with the Dirichlet boundary condition on a onedimensional domain (0, L). I will also study the bifurcation and stability of patterns in the n-dimensional Swift-Hohenberg equation with the odd-periodic and periodic boundary conditions....

Cyclicality and instability inherent in the economy can manifest themselves irregular fluctuations, including chaotic ones, which significantly reduces accuracy of forecasting dynamics economic system long run. We focus on an approach, associated with identification a deterministic endogenous mechanism fluctuations economy. Using mid-size firm model as example, we demonstrate use effective anal...