Abstract
Designing chaotic systems with different properties helps to increase our knowledge about real-world chaotic systems. In this article, a piecewise linear (PWL) term is employed to modify a simple chaotic system and obtain a new chaotic model. The proposed model does not have any equilibrium for different values of the control parameters. Therefore, its attractor is hidden. It is shown that the PWL term causes an offset boostable variable. This feature provides more flexibility and controllability in the designed system. Numerical analyses show that periodic and chaotic attractors coexist in some fixed values of the parameters, indicating multistability. Also, the feasibility of the system is approved by designing field programmable gate arrays (FPGA).
Highlights
Chaotic systems are characterized by sensitivity to initial conditions, known as the butterfly effect, and unpredictability
To analyze the effect of parameters of piecewise linear (PWL) term in the system dynamics, the bifurcation diagram of system (2) is plotted as the bifurcation parameter changes from −1 to 4.5 in Figure 3(a). e parameter b is 1, and the initial conditions are (−2.77, 0.53, 2.7, −0.34). e bifurcation diagram shows that the system exhibits both period-doubling and periodhalving routes to chaos in different parameter values
E proposed 4D PWL hyperjerk system is implemented in the field programmable gate arrays (FPGA) platform, which has high throughput and utilizes fewer resources. e system’s schematic and power analysis chart show the number of resources used for the implementation and its utilization percentage of power. e phase space diagram of the system is obtained using Xilinx System Generator tool [64, 66, 67]. is tool is integrated with MATLAB software, and a Simulink diagram is designed using Xilinx blocks which are readily available in the system generator tool kit
Summary
Chaotic systems are characterized by sensitivity to initial conditions, known as the butterfly effect, and unpredictability. About ten years ago, Leonov et al showed that the Chua’s circuit has another kind of attractor for which its basin of attraction does not collide with unstable manifolds [18]. Sometimes attractors coexist with each other and are characterized by the initial conditions Systems with these separated attractors (and their corresponding basins of attraction) are called multistable [27,28,29]. Different PWL systems have been proposed with multiscroll chaotic attractors and different numbers of equilibria [36, 37].
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