6.1 Introduction "Targeting" refers to a process wherein one uses a suitable sequence of small controlling perturbations to steer an initial condition on an attractor to a neighborhood of a prespecified point (target) on the attractor. Here it is shown that targeting can be done in high dimensional cases, as well for one-and two-dimensional maps. The method is demonstrated with a mechanical sys...

Periodic oscillations have been found in many different natural or physical systems, in particular biological organisms which have rhythmic phenomena at all levels with periods ranging from less than a second to years. From both theoretical and experiment viewpoints, it is a great challenging problem in biological science to model, analyze and further predict the periodic behaviors of living or...

The cytotoxic T lymphocyte (CTL) response to the infection of CD4+ T cells by human T cell leukemia virus type I (HTLV-I) has previously been modelled using standard response functions, with relatively simple dynamical outcomes. In this paper, we investigate the consequences of a more general CTL response and show that a sigmoidal response function gives rise to complex behaviours previously un...

This paper deals with the covariance control for discrete-time linear switched systems affected by additive stochastic noises. Given any periodic stabilizing switching law deterministic system associated to one, a finite set of matrices is characterized that an attractor state matrix sequence. Moreover, upper and lower bounds on are determined trajectories one-dimensional systems.

We study the periodic solutions of a discrete neuron model for period two or three parameter (internal decay rate) (βn)n=0∞. The novelty this research is finding chaotic attractor certain interval, outside defined interval solution goes to positive infinity negative infinity. investigation can be useful in design chaos-based neural networks architecture.

We prove that all algebraic bases β allow an eventually periodic representation of the elements ℚ(β) with a finite alphabet digits $${\cal A}$$ . Moreover, classification allowing those representations have socalled weak greedy property is given. The decision problem whether given pair (β, ) allows proves to be rather hard, for it equivalent topological attractor iterated function system.

The Milnor problem on one dimensional attractors is solved for S unimodal maps with a non degenerate critical point c It provides us with a complete understanding of the possible limit behavior for Lebesgue almost every point This theorem follows from a geometric study of the critical set c of a non renormalizable map It is proven that the scaling factors characterizing the geometry of this set...

We study the relations between the long-time dynamics of the Navier–Stokes-α model and the exact 3D Navier–Stokes system. We prove that bounded sets of solutions of the Navier–Stokes-α model converge to the trajectory attractor A0 of the 3D Navier–Stokes system as time tends to infinity and α approaches zero. In particular, we show that the trajectory attractor Aα of the Navier–Stokes-α model c...

When periodic current is injected into an integrate-and-fire model neuron, the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes. The attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtaine...