A dynamic antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space modelling by introducing the evolution of specificity of idiotypes. When the amount of external antigen increases, a measure of stability of the immune network is lost and thus the network can respond to the antigen. It is shown that specific and non-specific ...

Recently, the study of chaotic dynamics has evolved from the traditional trend of understanding and analyzing chaos to the new intention of controlling and utilizing it [Chen & Dong, 1998; Wang & Chen, 2000; Lü et al., 2002d]. The Lorenz system, found in 1963, produces the best-known canonical chaotic attractor in a simple three-dimensional autonomous system [Lorenz, 1963; Stewart, 2000]. In 19...

This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics ...

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...

A rigorous numerical algorithm, formally verified with Isabelle/HOL, is used to compute an accurate enclosure for the Lorenz attractor. Accurately enclosing the attractor is highly relevant: a similar non verified computation is part of Tucker’s proof that the Lorenz attractor is chaotic in a rigorous mathematical sense. This proof settled a conjecture that Fields medalist Stephen Smale has put...

This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivativ...

p-Ge electrically driven into the post-breakdown regime at liquid-He temperatures produces voltage oscillations which can be attributed to the formation of a chaotic attractor. Under variation of an applied magnetic field, a change in this attractor takes place which apparently reflects an increase in attractor dimensionality. A sequence of phase plots is presented which is interpreted as a tra...

A chaotic attractor may consist of some number of bands (disjoint connected subsets). In continuous maps multi-band chaotic attractors are cyclic, that means every generic trajectory visits the bands in the same order. We demonstrate that in discontinuous maps multi-band chaotic attractors may be acyclic. Additionally, a simple criterion is proposed which allows to distinguish easily between cy...

A crisis in chaotic dynamical systems is characterized by the conversion of a nonattracting, Cantorset-like chaotic saddle into a chaotic attractor. The gaps in between various pieces of the chaotic saddle are densely filled after the crisis. We give a quantitative scaling theory for the growth of the topological entropy for a major class of crises, the interior crisis. The theory is confirmed ...