Robust chaos is defined as the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space since the existence of such windows in the chaotic region implies fragility of the chaos. In this paper, we introduce a new terminology called robustification of chaos, which means creating robust chaos (in the sense of the above definition) in a dynamical system. As ...

This paper focuses on the decision-making behavior based on the complex adaptive system. Firstly, the paper reviewed the related work of the complex adaptive system and the edge of chaos in complex systems in different fields. Secondly, a general decision model of an agent is established and the condition that an agent is just at the edge of chaos is defined. Thirdly, making use of Langton’s co...

This brief studies the performance of selected chaos-based systems which share their frequency bands with conventional spread-spectrum systems. Such a scenario may occur in normal practice when chaos-based systems are introduced while the conventional systems are still in operation. The particular chaos-based systems under study are the coherent chaos-shift-keying system and the noncoherent dif...

In this paper, a new digital chaos circuit which can generate multiple-scroll strange attractors is proposed. Being based on the piecewise-linear function which is determined by on-chip supervised learning, the proposed digital chaos circuit can generate multiple-scroll strange attractors. Hence, the proposed circuit can exhibit various bifurcation phenomena. By numerical simulations, the learn...

The authors review the evidence for the applicability of random–matrix theory to nuclear spectra. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately: quantum chaos) in nuclei whenever random–matrix predictions are fulfilled. An introduction into the basic concepts of random–matrix theory is followed by a survey over the extant experimental information on spe...

We analyse a simple model of a digitally controlled mechanical system, which may perform chaotic vibrations. As a consequence of the digital effects, i.e., the sampling and the round-off error, the behaviour of this system can be described by the socalled micro-chaos map. If dry friction is present in the system, it can stop the motion. In such cases the resulting behaviour is referred to as tr...

Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titrati...

The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and suff...