Related papers: Distributional Chaos in Random Dynamical Systems
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
Empirical results show that PSO performance may be different if using either chaotic or random sequences to drive the algorithm's search dynamics. We analyze the phenomenon by evaluating the performance based on a benchmark of test…
In this letter we present a method of constructing dynamical systems with any preassigned number of equilibria by adding symmetry to another system with at least one equilibrium point. If the resulting system is chaotic, we call this…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
Two types of dynamics, chaotic and monotone, are compared. It is shown that monotone maps in strongly ordered spaces do not have chaotic attracting sets.
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios…
In the present study, we investigate the dynamics of impulsive differential equations driven by a chaotic system. We rigorously prove that, likewise the drive, the response impulsive system is also chaotic. Our results are based on the…
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems…
We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
This paper is concerned with Devaney chaos in non-autonomous discrete systems. It is shown that in its definition, the two former conditions, i.e., transitivity and density of periodic points, in a set imply the last one, i.e., sensitivity,…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
This paper discusses mixing of chaotic systems as a dependable method for secure communication. Distribution of the entropy function for steady state as well as plaintext input sequences are analyzed. It is shown that the mixing of chaotic…