Related papers: Advancing Chaos Theory: A Set-Valued Perspective o…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
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 investigate the structure of the invariant measure of space-time chaos by adopting an "open-system" point of view. We consider large but finite windows of formally infinite one-dimensional lattices and quantify the effect of the…
Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…
Traffic prediction in data-scarce, cross-city settings is challenging due to complex nonlinear dynamics and domain shifts. Existing methods often fail to capture traffic's inherent chaotic nature for effective few-shot learning. We propose…
In 2016, Hou and Wang introduced the concept of multiple mappings based on iterated function system, which is an important branch of fractal theory. In this paper, we introduce the definitions of sensitivity, accessibility, and Kato's chaos…
In this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proved that, under some conditions, these iterations have a chaotic…
Chaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global…
Design and cryptanalysis of chaotic encryption schemes are major concerns to provide secured information systems. Pursuing our previous research works, some well-defined discrete chaotic iterations that satisfy the reputed Devaney's…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
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…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
The onset of generalized synchronization of chaos in directionally-coupled systems corresponds to the formation of a continuous mapping which enables one to persistently define the state of the response system from the trajectory of the…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…
A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…