New realization of Chua's circuit and verification of chaos by harmonic balance analysis

Chua's circuit, which consists of two capacitors, one inductor, two resistors, one linear voltage-controlled voltage source (VCVS) and voltage-controlled current source (VCCS) type non-linear element has been realized by operational amplifiers. Various dynamical phenomena such as periodic orbit with periods T, 2T, and 4T, single scroll and double scroll similar to the Lorenz attractor have been observed experimentally by changing only the resistance value of the linear resistor R6. The experimental observations have been confirmed by computer simulations and also using harmonic balance analysis

Chaos control of a modified 4-D memristor chaotic oscillator via passive control technique

A modified memristor chaotic oscillator is proposed for a class of four dimensional chaotic systems. This modification can serve as an alternative way of designing the memristor circuit. We used the passive control technique which requires a single controller to stabilize the system which is presented in our numerical simulations for validation. Our results show that the passive control technique is a very effective technique for controlling chaotic systems.Keywords: Chaos; passive control; memristor; controllers; chaotic oscillator; nonlinear circui

Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters

A general critical condition of subharmonic oscillation in terms of the loop gain is derived. Many closed-form critical conditions for various control schemes in terms of converter parameters are also derived. Some previously known critical conditions become special cases in the generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme. Different control schemes share similar forms of critical conditions. For example, both V2 control and voltage mode control have the same form of critical condition. A peculiar phenomenon in average current mode control where subharmonic oscillation occurs in a window value of pole can be explained by the derived critical condition. A ripple amplitude index to predict subharmonic oscillation proposed in the past research has limited application and is shown invalid for a converter with a large pole.Comment: Submitted to an IEEE Journal on Dec. 23, 2011, and resubmitted to IEEE Transactions on Circuits and Systems-I on Feb. 14, 2012. My current six papers in arXiv have a common reviewe

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

Closed-Form Critical Conditions of Saddle-Node Bifurcations for Buck Converters

A general and exact critical condition of saddle-node bifurcation is derived in closed form for the buck converter. The critical condition is helpful for the converter designers to predict or prevent some jump instabilities or coexistence of multiple solutions associated with the saddle-node bifurcation. Some previously known critical conditions become special cases in this generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme.Comment: Submitted to IEEE Transactions on Automatic Control on Jan. 9, 2012. Seven of my arXiv manuscripts have a common reviewe

A note on the multi-stage spectral relaxation method for chaos control and synchronization

In this study, we present and apply a new, accurate and easy to implement numerical method to realize and verify the synchronization between two identical chaotic Lorenz, Genesio-Tesi, Rössler, Chen and Rikitake systems. The proposed method is called the multi-stage spectral relaxation method (MSRM). We utilize the active control technique for the synchronization of these systems. To illustrate the effectiveness of the method, simulation results are presented and compared with results obtained using the Runge-Kutta (4, 5) based MATLAB solver, ode45

Harmonic Balance-Based Approach for Quasi-Periodic Motions and Stability Analysis

Quasi-periodic motions and their stability are addressed from the point of view of different harmonic balance-based approaches. Two numerical methods are used: a generalized multidimensional version of harmonic balance and a modification of a classical solution by harmonic balance. The application to the case of a nonlinear response of a Duffing oscillator under a bi-periodic excitation has allowed a comparison of computational costs and stability evaluation results. The solutions issued from both methods are close to one another and time marching tests showing a good agreement with the harmonic balance results confirm these nonlinear responses. Besides the overall adequacy verification, the observation comparisons would underline the fact that while the 2D approach features better performance in resolution cost, the stability computation turns out to be of more interest to be conducted by the modified 1D approach

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

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