Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattractin...

We study a system of equations with discontinuous right hand side, which arise as models of gene and neural networks. Associated to the system is a graph of dynamics, which can be used to deene a Morse decomposition of the invariant set of the ow on the set of rays through the origin ((5]). We study attractors in R 4 which lie in a set of orthants in the form of gure eight. Trajectories can fol...

We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others. The existence of an alm...

|In this paper, we study the asymptotic behaviour of the solutions for the Benjamin-Bona-Mahony equation. We rst present the existence of the global weak attractor in H 2 per for this equation. And then by an energy equation we show that the global weak attractor is actually the global strong attractor in H 2 per. In this note, we consider the following Benjamin-Bona-Mahony equation: (1) with t...

Robust chaos occurs when a dynamical system has a neighborhood in parameter space such that there is one unique chaotic attractor, and no periodic attractors are present [Barreto et al., 1997; Banerjee et al., 19981. This behavior, expected to be relevant for any practical applications of chaos, was shown to exist in a general family of piecewise-smooth twodimensional maps, but conjectured to b...

We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than the more traditional approach of time averaging over a generic orbit. Finally, we discuss the relevance of the present work to the computatio...

We propose a robust method that allows a periodic or a chaotic multi-stable system to be transformed to a monostable system at an orbit with dominant frequency of any of the coexisting attractors. Our approach implies the selection of a particular attractor by periodic external modulation with frequency close to the dominant frequency in the power spectrum of a desired orbit and simultaneous an...

Abstract We use well-established methods of knot theory to study the topological structure of the set of periodic orbits of the Lü attractor. We show that, for a specific set of parameters, the Lü attractor is topologically different from the classical Lorenz attractor, whose dynamics is formed by a double cover of the simple horseshoe. This argues against the ‘similarity’ between the Lü and Lo...

In this paper we study the dynamics of a Burgers’ type equation (1.1). First, we use a new method called attractor bifurcation introduced by Ma and Wang in [4, 6] to study the bifurcation of Burgers’ type equation out of the trivial solution. For Dirichlet boundary condition, we get pitchfork attractor bifurcation as the parameter λ crosses the first eigenvalue. For periodic boundary condition,...

The response of model neurons driven by a periodic current converges onto mode-locked attractors. Reliability, de%ned as the noise stability of the attractor, was studied as a function of the drive frequency and noise strength. For weak noise, the neuron remained on one attractor and reliability was high. For intermediate noise strength, transitions between attractors occurred. For strong noise...