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A new two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium, its bifurcation analysis, circuit design and a control application to complete synchronization

Vaidyanathan Sundarapandian, Moroz Irene M., Sambas Aceng

Archives of Control Sciences

2023

Vol. 33, No. 2

277--298

In this work, we present new results for a two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium at the origin. The bifurcation and multi-stability analysis for the new hyperchaotic system are discussed in detail. As a control application, we develop a feedback control based on integral sliding mode control (ISMC) for the complete synchronization of a pair of two-scroll hyperchaotic systems developed in this work. Numerical simulations using Matlab are provided to illustrate the hyperchaotic phase portraits, bifurcation diagrams and synchronization results. Finally, as an electronic application, we simulate the new hyperchaotic system using Multisim for real-world implementations.

A new 4-D hyperchaotic four-wing system, its bifurcation analysis, complete synchronization and circuit simulation

Vaidyanathan Sundarapandian, Benkouider Khaled, Sambas Aceng, Safaan Samy Abdelwahab

Archives of Control Sciences

2022

Vol. 32, No. 3

507--534

In this work, we modify the dynamics of 3-D four-wing Li chaotic system (Li et al. 2015) by introducing a feedback controller and obtain a new 4-D hyperchaotic four-wing system with complex properties. We show that the new hyperchaotic four-wing system have three saddle-foci balance points, which are unstable. We carry out a detailed bifurcation analysis for the new hyperchaotic four-wing system and show that the hyperchaotic four-wing system has multistability and coexisting attractors. Using integral sliding mode control, we derive new results for the master-slave synchronization of hyperchaotic four-wing systems. Finally, we design an electronic circuit using MultiSim for real implementation of the new hyperchaotic four-wing system.

A new multistable double-scroll 4-D hyperchaotic system with no equilibrium point, its bifurcation analysis, synchronization and circuit design

Vaidyanathan Sundarapandian, He Shaobo, Simbas Aceng

Archives of Control Sciences

2021

Vol. 31, No. 1

99--128

In this work, we have developed a new 4-D dynamical system with hyperchaos and hidden attractor. First, by introducing a feedback input control into the 3-D Ma chaos system (2004), we obtain a new 4-D hyperchaos system with no equilibrium point. Thus, we derive a new hyperchaos system with hidden attractor. We carry out an extensive bifurcation analysis of the new hyperchaos model with respect to the three parameters. We also carry out probability density distribution analysis of the new hyperchaotic system. Interestingly, the new nonlinear hyperchaos system exhibits multistability with coexisting attractors. Next, we discuss global hyperchaos self-synchronization for the new hyperchaos system via Integral Sliding Mode Control (ISMC). As an engineering application, we realize the new 4-D hyperchaos system with an electronic circuit via MultiSim. The outputs of the MultiSim hyperchaos circuit show good match with the numerical MATLAB plots of the hyperchaos model. We also analyze the power spectral density (PSD) of the hyperchaos of the state variables using MultiSim.