A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation

This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility

A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via backstepping technique and MultiSim circuit design

This paper announces a new three-dimensional chaotic jerk system with two saddle-focus equilibrium points and gives a dynamic analysis of the properties of the jerk system such as Lyapunov exponents, phase portraits, Kaplan-Yorke dimension and equilibrium points. By modifying the Genesio-Tesi jerk dynamics (1992), a new jerk system is derived in this research study. The new jerk model is equipped with multistability and dissipative chaos with two saddle-foci equilibrium points. By invoking backstepping technique, new results for synchronizing chaos between the proposed jerk models are successfully yielded. MultiSim software is used to implement a circuit model for the new jerk dynamics. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical chaotic jerk model and the MultiSIM result

A New Chaotic System with Line of Equilibria: Dynamics, Passive Control and Circuit Design

A new chaotic system with line equilibrium is introduced in this paper. This system consists of five terms with two transcendental nonlinearities and two quadratic nonlinearities. Various tools of dynamical system such as phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and Poincarè map are used. It is interesting that this system has a line of fixed points and can display chaotic attractors. Next, this paper discusses control using passive control method. One example is given to insure the theoretical analysis. Finally, for the  new chaotic system, An electronic circuit for realizing the chaotic system has been implemented. The numerical simulation by using MATLAB 2010 and implementation of circuit simulations by using MultiSIM 10.0 have been performed in this study

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Symmetric oscillator: Special features, realization, and combination synchronization

Researchers have recently paid significant attention to special chaotic systems. In this work, we introduce an oscillator with different special features. In addition, the oscillator is symmetrical. The features and oscillator dynamics are discovered through different tools of nonlinear dynamics. An electronic circuit is designed to mimic the oscillator’s dynamics. Moreover, the combined synchronization of two drives and one response oscillator is reported. Numerical examples illustrate the correction of our approach.This work is partially funded by Centre for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2021/RD/064

UJI EFEKTIVITAS GENERATOR PEMBANGKIT SINYAL CHAOS DAN APLIKASINYA PADA KINEMATIKA ROBOT

Pada penelitian ini, kami akan menguji efektivitas sebuah sistem generator pembangkit sinyal chaos dalam pengontrolan kinematika robot. Generator pembangkit yang diusulkan adalah generator Moore-Spiegel. Studi awal penelitian ini adalah menganalisis sebuah model persamaan diferensial generator Moore-Spiegel dengan analisis titik equilibrium dan metode Runge Kutta orde 4. Selain itu, telah dikembangkan analisis lyapunov eksponen   untuk mengetahui interval peristiwa terjadinya sinyal chaos pada nilai tertentu. Hasil menunjukkan bahwa generator Moore-Spiegel memiliki strange attractor, Lyapunov eksponen positif yang mengindikasikan bahwa sistem berprilaku chaos. Model matematika dari generator Moore-Spiegel selanjutnya dibuat rancang bangun dengan menggunakan pendekatan analisis Op Amp dan analisis hukum Kirchoff. Simulasi numerik menggunakan MATLAB dan pendekatan validasi menggunakan MultiSIM menunjukkan kesesuaian prilaku sistem. Fokus terakhir penelitian ini adalah efektivitas parameter terjadinya sinyal chaos tersebut digunakan untuk mengontrol kinematika Robot. Hasil lintasan  yang diperoleh menggunakan sistem kontrol persamaan generator Moore-Spiegel menunjukkan presentase 60% dalam scaning area. Berdasarkan persentase tersebut, generator Moore-Spiegel sangat baik untuk dijadikan sistem kontrol dalam kinematika robot