Chaotic Dynamics in Discrete Time Systems

Dear Colleagues,

The study of chaos theory emerged from continuous dynamical systems, but it is also comprehensively documented in discrete time. Here, chaotic behavior can be present even in one-dimensional systems, in contrast to continuous time, where a minimum of three dimensions is required. Due to their ease of implementation and low computational cost, discrete chaotic systems, or chaotic maps as they are also termed, are often opted in applications where speed and computational load are of importance.

Nonetheless, apart from their adequacy in applications, discrete-time systems are also studied for their rich dynamical properties, found often to be universal to many nonlinear dynamical systems. Discrete-time chaotic systems can exhibit a wide variety of chaos-related phenomena, with regards to their transition to (and from) chaos, the number of equilibria and their stability, the existence of symmetric behavior, coexisting behaviors, and more. They also allow for rigorous demonstrations of universal fundamental phenomena in nonlinear dynamics.

This Special Issue aims to explore chaotic phenomena in discrete-time systems. Authors are welcome to submit their original and review works on discrete-time systems of any dimension which showcase interesting chaotic phenomena. Examples include:

• Symmetric attractors;
• Coexisting attractors;
• Hidden attractors;
• Antimonotonicity;
• Crisis;
• Bifurcations;
• Decay of correlations;
• Transient dynamics;
• Networks and multilayer networks of chaotic maps;
• Robust chaos;
• Infinite number of equilibria;
• Controllable number of equilibria;
• Controllable statistical measures;
• Techniques for constructing new maps;
• Novel tools and measures for studying chaotic maps;
• Digital implementations of the above;
• Applications of chaotic maps and their transformed versions in optimization, encryption, communications, and more.

Dr. Lazaros Moysis
Dr. Marcin Lawnik
Dr. Murilo da Silva Baptista
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Dynamics is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• chaos
• discrete time
• map
• bifurcation
• attractors
• applications
• equilibria
• lyapunov exponent
• chaotification
• symmetry
• coexisting attractor