A new two-scroll chaotic system with two nonlinearities: dynamical analysis and circuit simulation

Chaos theory has several applications in science and engineering. In this work, we announce a new two-scroll chaotic system with two nonlinearities. The dynamical properties of the system such as dissipativity, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension and bifurcation diagram are explored in detail. The presence of coexisting chaotic attractors, coexisting chaotic and periodic attractors in the system is also investigated. In addition, the offset boosting of a variable in the new chaotic system is achieved by adding a single controlled constant. It is shown that the new chaotic system has rotation symmetry about the z-axis. An electronic circuit simulation of the new two-scroll chaotic system is built using Multisim to check the feasibility of the theoretical model.

MODEL MATEMATIK DAN ANALISIS SIRKUIT GENESIOTESI DALAM SISTEM KEMANAN KOMUNIKASI SUARA

Dalam pekerjaan ini, sistem chaos Genesio-Tesi dengan satu istilah kuadrat telah diusulkan, dan sifat kualitatif telah ditunjukkan secara rinci. Perilaku dinamis dari sirkui Genesio-Tesi telah dianalisis. Khususnya, spektrum Lyapunov eksponen, struktur eigen, diagram bifurkasi dan peta Poincare. Pelaksanaan sirkuit elektronik Genesio-Tesi telah dirancang dan disimulasikan dalam Multisim. Sistem ini diimplementasikan sebagai sebuah sirkuit elektronik yang perilakunya menegaskan prediksi numerik. Selanjutnya, efektivitas sinkronisasi antara dua sistem sirkuit Genesio-Tesi yang identik dalam sistem keamanan komunikasi suara telah disajikan dalam pekerjaan ini. Akhirnya, tehnik sinkronisasi yang baik menunjukkan bahwa sirkuit Genesio-Tesi berpotensi besar dalam perkembangan sistem kemanan komunikasi berbasis suara. Integrasi fisika teoritis, simulasi numerik menggunakan MATLAB serta implementasi simulasi sirkuit menggunakan MultiSIM dan rancang bangun elektronik telah dilakukan dalam makalah ini

Hybrid Chaos Synchronization of 3-Cells Cellular Neural Network Attractors via Adaptive Control Method

Abstract: In this research work, we first discuss the properties of the 3-cells cellular neural network (CNN) attractor discovered b

MODEL MATEMATIK DAN ANALISIS SIRKUIT GENESIOTESI DALAM SISTEM KEMANAN KOMUNIKASI SUARA

Dalam pekerjaan ini, sistem chaos Genesio-Tesi dengan satu istilah kuadrat telah diusulkan, dan sifat kualitatif telah ditunjukkan secara rinci. Perilaku dinamis dari sirkui Genesio-Tesi telah dianalisis. Khususnya, spektrum Lyapunov eksponen, struktur eigen, diagram bifurkasi dan peta Poincare. Pelaksanaan sirkuit elektronik Genesio-Tesi telah dirancang dan disimulasikan dalam Multisim. Sistem ini diimplementasikan sebagai sebuah sirkuit elektronik yang perilakunya menegaskan prediksi numerik. Selanjutnya, efektivitas sinkronisasi antara dua sistem sirkuit Genesio-Tesi yang identik dalam sistem keamanan komunikasi suara telah disajikan dalam pekerjaan ini. Akhirnya, tehnik sinkronisasi yang baik menunjukkan bahwa sirkuit Genesio-Tesi berpotensi besar dalam perkembangan sistem kemanan komunikasi berbasis suara. Integrasi fisika teoritis, simulasi numerik menggunakan MATLAB serta implementasi simulasi sirkuit menggunakan MultiSIM dan rancang bangun elektronik telah dilakukan dalam makalah ini

Rikitake dynamo system, its circuit simulation and chaotic synchronization via quasi-sliding mode control

Rikitake dynamo system (1958) is a famous two-disk dynamo model that is capable of executing nonlinear chaotic oscillations similar to the chaotic oscillations as revealed by palaeomagnetic study. First, we detail the Rikitake dynamo system, its signal plots and important dynamic properties. Then a circuit design using Multisim is carried out for the Rikitake dynamo system. New synchronous quasi-sliding mode control (QSMC) for Rikitake chaotic system is studied in this paper. Furthermore, the selection on switching surface and the existence of QSMC scheme is also designed in this paper. The efficiency of the QSMC scheme is illustrated with MATLAB plots

Hybrid Synchronization of the Generalized Lotka-Volterra Three-Species Biological Systems via Adaptive Control

Abstract: Since the recent research has shown the importance of biological control in many biological systems appearing in nature, this research paper investigates research in the dynamic and chaotic analysis of the generalized Lotka-Volterra three-species biological system, which was studied b

A new buffering theory of social support and psychological stress

A dynamical model linking stress, social support, and health has been recently proposed and numerically analyzed from a classical point of view of integer-order calculus. Although interesting observations have been obtained in this way, the present work conducts a fractional-order analysis of that model. Under a periodic forcing of an environmental stress variable, the perceived stress has been analyzed through bifurcation diagrams and two well-known metrics of entropy and complexity, such as spectral entropy and C0 complexity. The results obtained by numerical simulations have shown novel insights into how stress evolves with frequency and amplitude of the perturbation, as well as with initial conditions for the system variables. More precisely, it has been observed that stress can alternate between chaos, periodic oscillations, and stable behaviors as the fractional order varies. Moreover, the perturbation frequency has revealed a narrow interval for the chaotic oscillations, while its amplitude may present different values indicating a low sensitivity regarding chaos generation. Also, the perceived stress has been noted to be highly sensitive to initial conditions for the symptoms of stress-related ill-health and for the social support received from family and friends. This work opens new directions of research whereby fractional calculus might offer more insight into psychology, life sciences, mental disorders, and stress-free well-being

Hyperchaotic Attractor in a Novel Hyperjerk System with Two Nonlinearities

Hyperjerk systems have received considerable interest in the literature because of their simplicity and complex dynamical properties. In this work, we introduce a novel hyperjerk system with an absolute nonlinearity and a quintic term. Interestingly, the hyperjerk system exhibits hyperchaotic behavior. Dynamics and the feasibility of the hyperjerk system are discovered by using numerical analysis and circuit implementation. Moreover, adaptive controllers have been designed for stabilization and synchronization of the new hyperjerk system. The control results have been established by using Lyapunov stability theory, and numerical simulations with MATLAB have been shown to illustrate the validity of the constructed adaptive controllers. © 2017, Springer Science+Business Media New York