We report on the observation of noise-free stochastic resonance in an externally driven diode resonator close to an interior crisis. At sufficiently high excitation amplitudes the diode resonator shows a strange attractor which after the collision with an unstable period-three orbit exhibits crisis-induced intermittency. In the intermittency regime the system jumps between the previously stable...

Recent progress towards an understanding of fluctuational escape from chaotic attractors (CAs) is reviewed and discussed in the contexts of both continuous systems and maps. It is shown that, like the simpler case of escape from a regular attractor, a unique most probable escape path (MPEP) is followed from a CA to the boundary of its basin of attraction. This remains true even where the bounda...

The origin of log-periodic oscillations around the power-law trend of the escape probability from a precritical attractor and of the noise-free stochastic multiresonance, found in numerical simulations in chaotic systems close to crises is discussed. It is shown that multiple maxima of the spectral power amplification vs. the control parameter result from a fractal structure of a precritical at...

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windo...

We introduce and study properties of phyllotactic and rhombic tilings on the cylinder. These are discrete sets of points that generalize cylindrical lattices. Rhombic tilings appear as periodic orbits of a discrete dynamical system S that models plant pattern formation by stacking disks of equal radius on the cylinder. This system has the advantage of allowing several disks at the same level, a...

Of interest is the dynamics of discrete-time amensalism model with a cover on first species. We obtain existence and stability fixed points conditions for permanent coexistence two Then we demonstrate occurrence flip bifurcation by using central manifold theorem theory. A hybrid control strategy used to stabilize unstable periodic orbits embedded in complex attractor. Numerical simulation verif...

The parameter perturbation methods (the most known being the OGY method) apply small wisely chosen swift kicks to the system once per cycle, to maintain it near the desired unstable periodic orbit. Thus, one can consider that a new attractor is finally generated. Another class of methods which allow the attractors born, imply small perturbations of the state variable [see, e.g., J. Güémez and M...

In this article, we stress the need for using dy-namical systems properties in autonomous architecture design. We rst study the dynamics of random recurrent neural networks (RRNN). Such systems are known to spontaneously exhibits various dynamical regimes, as they always tries to remain on an attractor, thus achieving stable dy-namical behaviors. Second, we try to characterize the adaptive prop...

The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector φ1 of ...

The effect of the shape of six different periodic forces and second periodic forces on the onset of horseshoe chaos are studied both analytically and numerically in a Duffing oscillator. The external periodic forces considered are sine wave, square wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectified sine wave, and modulus of sine wave. An analytical threshold condition for the ...