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In this paper a new 5D chaotic system with line equilibrium is designed and described to reveal its extreme multi-stability. Hence, all of the resulting attractors are hidden. The suggested system owns many complex dynamic behaviors in comparison with other chaotic systems. System initial state-associated complex dynamical behaviors are considered and we discover that it possesses an immeasurable number of coexisting attractors, which expresses the occurrence of extreme multi-stability. Besides, we also demonstrate the line equilibrium stability in detail, bifurcation diagrams, Lyapunov exponents, and basins of attraction. Also, in order to analyze the new 5D chaotic system we have considered the permutation entropy technique. Finally, the application of the novel 5D chaotic system with line equilibrium to the problem of chaos synchronization and secure communication through observer design is presented. [ABSTRACT FROM AUTHOR]

Multistability is an essential topic in nonlinear dynamics. Recently, two critical subsets of multistable systems have been introduced: systems with extreme multistability and systems with megastability. In this paper, based on a newly introduced megastable system, a megastable forced oscillator is introduced. The effect of adding a forcing term and its parameters on the dynamical behavior of the designed system is investigated. By the help of bifurcation diagram and Lyapunov exponents, it is shown that the modified oscillator can show a variety of dynamical solutions including limit cycle, torus, and strange attractor. [ABSTRACT FROM AUTHOR]

A new 4-D memristive chaotic flow is proposed in this paper. Dynamical investigation of the proposed system shows some specific properties. The system has a line of equilibria which are unstable in some limited intervals and stable at other intervals. Investigating bifurcation diagram of the system shows an inverse period-doubling route to chaos. Also, different initiation in plotting bifurcation diagram shows its multistability. In some intervals of the parameter, two Lyapunov exponents of the system are positive, and the attractor is hyper-chaotic. However, in some other ranges of parameters, only one Lyapunov exponent is positive, and the attractor is chaotic. Basin of attraction of the system is studied which shows a vast region of attraction for the chaotic attractor. Entropy analysis of the system provides a viewpoint into the unpredictability of the system. [ABSTRACT FROM AUTHOR]

In this paper, a new four-dimensional nonlinear oscillator is introduced. This oscillator is memristive and can exhibit chaotic behavior. A complete dynamical analysis is done on each parameter of this system by the help of bifurcation diagram and Lyapunov exponents' diagram. In order to estimate parameters of the proposed system, we use a new cost function based on the similarity between return maps. Then, with the help of ions motion optimization method, we minimize the obtained cost function and find the exact value of parameters. [ABSTRACT FROM AUTHOR]

In this paper, by modifying a known two-dimensional oscillator, we obtain an interesting new oscillator with coexisting limit cycles and point attractors. Then by changing this new system to its forced version and choosing a proper set of parameters, we introduce a chaotic system with some very interesting features. In this system, not only can we see the coexistence of different types of attractors, but also a fascinating phenomenon: some initial conditions can escape from the gravity of nearby attractors and travel far away before being trapped in an attractor beyond the usual access. [ABSTRACT FROM AUTHOR]

Abstract Analyzing chaotic systems with coexisting and hidden attractors has been receiving much attention recently. In this article, we analyze a four dimensional chaotic system which has a plane as the equilibrium points. Also this system is of the group of systems that have coexisting attractors. First, the system is introduced and then stability analysis, bifurcation diagram and Largest Lyapunov exponent of this system are presented as methods to analyze the multistability of the system. These methods reveal that in some ranges of the parameter, this chaotic system has three different types of coexisting attractors, chaotic, stable node and limit cycle. Some interesting dynamics properties such as reversals of period doubling bifurcation and offset boosting are also presented. Highlights • We analyze a four dimensional chaotic system which has a plane as the equilibrium points. • The analysis reveals the coexistence of various types of attractors including chaotic and periodic ones. • Period-doubling bifurcations and offset boosting are also reported when monitoring the system parameters. [ABSTRACT FROM AUTHOR]