Constructing multiwing attractors from a robust chaotic system with non-hyperbolic equilibrium points

We investigate a three-dimensional (3D) robust chaotic system which only holds two nonhyperbolic equilibrium points, and finds the complex dynamical behaviour of position modulation beyond amplitude modulation. To extend the application of this chaotic system, we initiate a novel methodology to construct multiwing chaotic attractors by modifying the position and amplitude parameters. Moreover, the signal amplitude, range and distance of the generated multiwings can be easily adjusted by using the control parameters, which enable us to enhance the potential application in chaotic cryptography and secure communication. The effectiveness of the theoretical analyses is confirmed by numerical simulations. Particularly, the multiwing attractor is physically realized by using DSP (digital signal processor) chip

Grid Multiscroll Hyperchaotic Attractors Based on Colpitts Oscillator Mode with Controllable Grid Gradient and Scroll Numbers

AbstractThrough introducing two piecewise-linear triangular wave functions in a three-dimensional spiral chaotic Colpitts oscillator model, a four-dimensional grid multiscroll hyperchaotic system is constructed. Interestingly, by adjusting a build-in parameter in a variable of one triangle wave function, the control of the gradient of the multiscroll grid is achieved. Whereas by deploying the zero points of the two triangular wave functions to extend the saddle-focus equilibrium points with index-2 in phase space the scroll numbers do not only increase along with the number of turning points, but they can also generate arbitrary multiples of products. The basic dynamical behaviors of the proposed four-dimensional multiscroll hyperchaotic system are analyzed. Finally, the hardware experimental circuit is designed and the interrelated circuit implementation is realized. The experimental results are in agreement with both theoretical analyses and numerical simulations, which verify the feasibility of the design methods

Analysis of a class of complex system without equilibria via switched control law

"In this article we introduce a new class of complex system without equilibria which exhibits a chaotic multiscroll attractor in each node. The number of scrolls in the attractor is determined by a switched control law to allow the operation of different linear affine systems. Thus, the system is composed of many subsystems which interact with each other to generate a multiscroll attractor. This new class of piecewise linear (PWL) system presents no positive real part in the eigenvalues of the Jacobian matrix as opposed to the reported systems with multiscrolls. The scrolls present a complex behavior since these don’t unwrap and don’t appear close to an unstable manifold of a saddle-focus equilibrium point. A particular case is taken as case study and simulation plots of the attractor are provided.

Grid multi-wing butterfly chaotic attractors generated from a new 3-D quadratic autonomous system

Due to the dynamic characteristics of the Lorenz system, multi-wing chaotic systems are still confined in the positive half-space and fail to break the threshold limit. In this paper, a new approach for generating complex grid multi-wing attractors that can break the threshold limit via a novel nonlinear modulating function is proposed from the firstly proposed double-wing chaotic system. The proposed method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. The new system is autonomous and can generate various grid multi-wing butterfly chaotic attractors without requiring any external forcing, it also can produce grid multi-wing both on the xz-plane and yz-plane. Basic properties of the new system such as dissipation property, equilibrium, stability, the Lyapunov exponent spectrum and bifurcation diagram are introduced by numerical simulation, theoretical analysis and circuit experiment, which confirm that the multi-wing attractors chaotic system has more rich and complicated chaotic dynamics. Finally, a novel module-based unified circuit is designed which provides some principles and guidelines for future circuitry design and engineering application. The circuit experimental results are consistent with the numerical simulation results.&nbsp

Design of time delayed chaotic circuit with threshold controller

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.Comment: 21 pages, 12 figures; Submitted to IJB

A universal variable extension method for designing multi-scroll/wing chaotic systems

© 2023 IEEE. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1109/TIE.2023.3299020Developing a universal design method to construct different multiscroll/wing chaotic systems (MS/WCSs) has been challenging. This article proposes a general design method for MS $/$ WCSs called the universal variable extension method (UVEM). It is a simple but effective approach that generates one-direction (1-D) and 2-D multiscroll/wing chaotic attractors. Using any double-scroll/wing chaotic system as the basic system, the UVEM is able to construct different MS/WCSs. Employing Chua's chaotic system and Lorenz chaotic system as two examples, we construct two MSCSs (including 1-D and 2-D) and two MWCSs (including 1-D and 2-D), respectively. Theoretical analysis and numerical simulation show that the constructed MS/WCSs not only can generate 1-D and 2-D multiscroll/wing chaotic attractors but also have 1-D and 2-D initial boosting behaviors. This means that the MS/WCSs designed by the UVEM are very sensitive to their initial states, and have better unpredictability and more complex chaotic behaviors. To show the simplicity of UVEM in hardware implementation, we develop a field-programmable gate array-based digital hardware platform to implement the designed MS $/$ WCSs. Finally, a new pseudorandom number generator is proposed to investigate the application of the MS/WCSs. All P-values obtained by the NIST SP800-22 test are larger than 0.01, which indicates that the MS/WCSs designed by UVEM have high randomness.Peer reviewe