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Special Topics

# EPJ ST Special Issue: Special Chaotic Systems

For many years, researchers have believed that the formation of strange attractors in a dynamical system is related to a saddle point in its structure. Many well-known systems with chaotic attractors such as Lorenz, Rossler, and Chen system have a saddle point equilibria. This category of chaotic attractors is familiar and finding their chaotic attractors are easy since they are formed near the saddle points. In other words, most chaotic systems have a strange attractor around their saddle point equilibria and can be easily designed. In 2011, Sprott presented some standards to propose new systems with strange attractors. He proposed that a new chaotic system should satisfy at least one of the following three conditions: First, the proposed systems should model some important unsolved problem in nature. Second, the systems should exhibit some behavior previously unobserved. Finally, the system should be simpler than all other known examples exhibiting the observed behavior. For example, the Lorenz system satisfy all of those conditions in its first publication in 1963.

In the last decade, some novel dynamical systems with chaotic attractor have been found that did not have any saddle point equilibria. Till now many new chaotic systems have been proposed in this category. We call those systems “special”. In other words, chaotic systems which satisfy the novelty conditions and are not common, are in this category. Chaotic systems without any equilibria, chaotic systems with a line of equilibria, chaotic systems with curve of equilibria, and with surfaces of equilibria are in this category.

The dynamic of chaotic systems depends on the initial conditions as well as parameters. So a system can show different coexisting attractors in the constant parameters just by varying initial conditions. Such a system is called “multi-stable”. A system which has countable infinity of coexisting attractors are called “mega-stable”, while systems with uncountable infinity of coexisting attractors are called “extreme multi-stable”. Chaotic systems with different multi-stabilities can satisfy the novelty conditions of the standard of proposing chaotic systems. Another interesting dynamic in the special chaotic systems is the coexistence of symmetric attractors.

Chaotic attractors can be categorize into self-excited or hidden attractors. Self-excited attractors are those attractors which their basin of attraction contains an unstable equilibrium while the basin of attraction in hidden attractors are not related to any equilibrium point. Hidden chaotic attractors are one of the hottest topics in the study of special chaotic systems. Many novel systems have been proposed with hidden attractors. Rare attractors are those attractors in which their basins of attraction are very small. Chaotic systems with rare attractors has attracted lots of attentions. Systems with multi-scroll chaotic attractors are other interesting dynamical systems. However, in the study of novel chaotic attractors with any special property, it is very important that the system be the simplest one with that feature.

Chaotic systems can be categorized based on their dissipation. A system is called conservative if its dissipation is zero. Some systems are “nonuniformly conservative”. It means that they are globally conservative, but they have some regions of state space in which the system is dissipative and some other regions which is anti-dissipative. Also, there are some other features which are worth in the study of new chaotic systems.

Call for papers: We would like to cordially invite further authors to submit their original research papers for this special issue along the lines described above. An extended description of the critical aspects/open problems of the methods presented will be a stringent criterion of pre-selection of papers to be sent to referees. Articles may be one of four types: (i) minireviews (10-15 pages), (ii) tutorial reviews (15+ pages), (iii) original paper v1 (5-10 pages), or (iv) original paper v2 (3-5 pages). More detailed descriptions of each paper type can be found here. Manuscripts should be prepared using the latex template of EPJ ST, which can be downloaded here. Articles should be submitted to the Editorial Office of EPJ ST by selecting "Special Chaotic Systems" as a special issue at:https://articlestatus.edpsciences.org/is/epjst/home.php

Guest Editors: Tomasz Kapitaniak (Division of Dynamics, Technical University of Lodz, Lodz, Poland) and Sajad Jafari (Biomedical Engineering Department, Amirkabir University of Technology, Tehran, Iran)