Hidden Coexisting Attractors in a Chaotic System Without Equilibrium Point

Abstract

This paper proposes a new three-dimensional chaotic system with no equilibrium point but can generate hidden chaotic attractors. Dynamic characteristics of the system are analyzed in detail by theoretical analysis and simulating experiments, including hidden attractors, transient period and coexisting attractors. Different hidden coexisting attractors exist in this system, which shows abundant and complex dynamic characteristics and can be used to generate pseudorandom sequences for encryption fields. Besides, the presented system is realized by the digital signal processing (DSP) technology to construct a chaotic signal generator, whose statistical properties are tested by National Institute of Standards and Technology (NIST) software. The obtained results are better than that of the Lorenz system and imply the presented system can be used in the encrypted fields.

Antimonotonicity, Chaos and Multidirectional Scroll Attractor in Autonomous ODEs Chaotic System

“…Subsequently, many literatures were found the various types of scroll attractors are based on nonlinear function, such as the sinusoidal [16], trigonometric [17], transformations [18], piecewise [19], [23], saturation, sign [20]- [22], tangent, multi-fold surface, wings forms of scroll attractors [25], and so on [21]- [24]. However, the highly complex dynamics, such as antimonotonicity [26]- [28] and coexisting attractors [29], [30], [35], [44], as a new research direction, are…”

“…Then, the rich dynamic behaviors including antimonotonicity (i.e. concurrent creation and annihilation of periodic orbits) [26]- [28], hidden coexisting attractors [29], basins of various coexisting attractors [30]- [32] and multistability [33] are analyzed. In addition, butterfly attractors are emerged from Lorenz-like system and coexisting attractors are spotted.…”

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

“…The coexistence of self-excited attractors or hidden attractors has been found in various kinds of continuous ordinary differential systems. These ordinary differential systems contain the purely mathematical chaotic and hyperchaotic systems [ 8 , 9 ], memristor-based chaotic circuits and systems [ 10 , 11 ], and Hopfield neural networks [ 12 , 13 ]. When the coexisting attractors reach an infinite number, this phenomenon is defined as extreme multistability [ 14 ], which has been reported in many memristor-based chaotic systems [ 15 , 16 ].…”

Bounded Orbits and Multiple Scroll Coexisting Attractors in a Dual System of Chua System

“…some scholars and their co-workers proposed plenty of methods for designing the grid multi-scroll and multi-wing chaotic and hyper chaotic attractors [4,5,9,[29][30][31], L. Zhou and his fellows proposed a novel no-equilibrium hyper chaotic system [10], J. Kengne et al presented dynamics for Jerk or Jerk-like system with multiple attractors [11,12,19], Q. Lai and S. Chen proposed a polynomial function method for generating multiple strange attractors from the Sprott B system [31], just to name a few; (ii) all kinds of analysis methods have been described on unusual and striking dynamics, such as the, self-excited antimonotonicity [11,14,21] and hidden attractors [15], coexisting attractors [16][17][18][19][22][23][24], without equilibrium chaotic system [10,18,19], and multiple stability [20] and synchronization [8,33] as new research directions, are still in their infancy. Especially, in n-scroll chaotic system, the occurrence of two or more asymptotically stable or attracting basin have been analyzed, symmetry and broken symmetry have been reported.…”