Generating novel multi-scroll chaotic attractors via fractal transformation

Abstract

The fractal and chaos are bound tightly, and their relevant researches are well-established. Few of them, however, concentrates on the research of the possibility of combining the fractal and the chaotic systems to generate multi-scroll chaotic attractors. This paper presents a novel non-equilibrium point chaotic system, exhibiting extremely rich and complex hidden behaviors including chaos, hyper-chaos, multiscroll attractors, extreme multi-stability and initial offset-boosting. The proposed system is combined with fractal transformation respectively, and a new class of multi-scroll attractors, such as multi-ring attractors and separated-scroll attractors, is observed. Particularly, swallow-shaped attractors for the first time is found. Moreover, another efficient method to generate a different class of chaotic attractors uses parabola transformation and triangle transformation. Additionally, the spectrum entropy (SE) complexity is employed to discuss the complexity of the proposed system before and after fractal, resulting in a chaotic sequences with fractal transformation that has higher complexity. Finally, we develop a hardware platform to implement the presented attractors before and after fractal in a way to confirm the accuracy of the numerical simulations, providing a theoretical basis for the next application in image encryption.

A Universal Variable Extension Method for Designing Multiscroll/Wing Chaotic Systems

“…For example, in traditional methods, the basic double-scroll/wing systems must be changed. In most existing methods [4,18,24,29], the control parameters are non-integral, which makes it very difficult to adjust chaotic attractors. on the contrary, the UVEM is no need to change the original basic systems and only requires integer parameters.…”

“…Finally, the 17th-32nd bits from the bit stream are truncated as pseudorandom numbers. The designed PRNG can be described as P i = B(s n ) 17:32 (29) where B(.) is to transform a value into a 32-bit float number obeying the IEEE floating point standard, and P is the obtained random number sequence.…”

“…Zhang et al [3,27] proposed an MSCS and an MWCS by coupling a multipiecewise linear memristor into a Jerk system and a Sprott system, respectively. Moreover, some other approaches like symmetry conversion [28], fractal transformation [29], and neural networks [30,31] have also been reported.…”

A physical memristor-based chaotic system and its application in colour image encryption scheme

“…Due to its complex characteristics, the chaotic system has several applications in medicine [1], biological science [2], geology [3], physics [4], secure information encryption [5,6], pseudo-random number generation [7], noise removal [8] etc The generation of multi-scroll or multi-wing attractors is a promising way to increase the complexity of the chaotic systems, which also influences the generation of many random keys. This complexity can be utilized by observing the shifting nature of the chaotic system from one scroll to another scroll in the phase trajectory [9][10][11][12][13]. Memristor has a remarkable contribution in synthesizing neuronal activities in a dynamical model.…”

Scroll-growing/controlling chaotic attractors in cyclic Hopfield neural networks via memristive bridging

“…Among these chaotic systems, multi-scroll chaotic systems (MSCSs) are a special class of dynamical systems, which have more complex attractive domains and phase spaces than conventional chaotic systems, and are more suitable for many practical applications, such as pseudorandom bit generator [5], image encryption [6,7], medical digital image watermarking [8], weak signal detection [9], and medical privacy protection [10]. Because of this, how to design a MSCS is an important research topic that deserves attention [11][12][13][14][15].…”