Related papers: Topological chaos and chaotic iterations. Applicat…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…
In recent years, a lot of research has gone into creating multi-layer chaotic mapping-based cryptosystems. Random-like behavior, a continuous broadband power spectrum, and a weak baseline condition dependency are all characteristics of…
It was recently shown (quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
The main theorem of this paper establishes conditions under which the "chaos game" algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non contractive iterated…
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability,…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…
It has been demonstrated earlier that universal computation is 'almost surely' chaotic. Machine learning is a form of computational fixed point iteration, iterating over the computable function space. We showcase some properties of this…
Chaos is a phenomenon that attracted much attention in the past ten years. In this paper, we analyze chaos-based signal processing, and proposed a chaos processor to take advantage of chaos phenomenon. We also analyzed and demonstrated two…
Cryptography is always very important in data origin authentications, entity authentication, data integrity and confidentiality. In recent years, a variety of chaotic cryptographic schemes have been proposed. These schemes have typical…
This paper studies the security of a secure communication scheme based on two discrete-time intermittently-chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) the key space…
In this paper we propose, discuss and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers and non-periodically forced…
We discuss Devaney chaos on compact metric spaces using a decomposition space characterized by topological nature of symbolic dynamics. A chaotic map obtained here is defined as a topologically conjugate of the chaotic map on a…
We present a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems.
In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…