Let X be a compact metric space, let φ be a continuous self-map on X , and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between various dynamical properties of a given (crisp) dynamical system (X,φ) and its Zadeh’s extension Φ on F(X). Among other things we study various (weak, strong, mild etc.) mixing properties and also s...

Lasers are essentially chaotic system. However, semiconductor lasers are classified into stable class B lasers. Meanwhile, they are easily destabilized by external perturbations (introduction of extra degree of freedom). We discuss chaos in lasers and also instability and chaos in semiconductor lasers. Recently, new semiconductor lasers with extra device structures have been developed and they ...

Precisely describing the formation and evolution rules of coal-rock fracturing crack have great value on reservoir fracturing improvement and highly efficient mining of coal bed methane well. In this paper, a non-linear dynamic method is used to study crack damage evolution behavior of coal-rock fracturing. Considering distribution characteristics of natural cracks in coal-rock, and based on da...

With the aid of an original reformulation of the KAM theory, it is shown that a relevant control of Hamiltonian chaos is possible through suitable small perturbations whose form can be explicitly computed. In particular, it is shown that it is possible to control (reduce) the chaotic diffusion in the phase space of a 1.5 degrees of freedom Hamiltonian which models the diffusion of charged test ...

This paper aims at a historical and pedagogical presentation of some important contributions of the research on thermonuclear fusion by magnetic confinement to the study of Hamiltonian chaos. This chaos is defined with the help of Poincaré maps on a simple two-wave Hamiltonian system. A simple criterion for computing the transition to large scale chaos is introduced. A renormalization group app...

The theory of chaos and shadowing developed recently by the author is amplified to the case of a heteroclinically tubular cycle. Specifically, let F be a C3 diffeomorphism on a Banach space. F has a heteroclinically tubular cycle that connects two normally hyperbolic invariant manifolds. Around the heteroclinically tubular cycle, a Bernoulli shift dynamics of submanifolds is established through...

Hyper chaos is the non-periodic behaviour of deterministic nonlinear dynamical system that is highly sensitive to initial conditions with more than one positive Lypunov Exponents, i.e., its dynamics expand not only small line segments, but also small area elements, these giving rise to a ‘thick’ chaotic attractor. Bifurcation effects include the period doubling route to chaos, the intermittency...

This paper studies chaos synchronization in the modified Chua's circuit with x x using linear state feedback control scheme. A new sufficient condition is derived for chaos synchronization between the two modified Chua's circuits with x x based on the Lyapunov stability theory and the Linear Quadratic Optimal Control theory. A simulation example is given for demonstration. 1. Introduction Today...

In view of the importance of noi se in physiology. information processing and fi nance, studi es on chaos and noi se have been undertaken. Detailed stud ies on the lal lowing osc illatory reactions have been undertaken: (i) thi ophenol + BrO,' + H2S0~, (ii ) fruClose + BrO,' + H2S04 + Ce 4 + , and (iii ) iodate + arsenitc, wh ich can serve as a model system for thi s purposc. Aperiodic oscil la...