Bifurcation Analysis of a Class Fractional-Oder Nonlinear Chua's Circuit System

In recent years, with the rapid development of science and technology, dynamic characterization and control of the research circuit system has become not only theoretical but also practical consideration in academic research and practical engineering applications. Therefore, the complex behavior of a research circuit system has become a hot spot in the theoretical field. This thesis is aimed toward the stability criterion and bifurcation of the fractional-order Chua’s circuit system. Despite numerous studies relating to the Chua’s system, most of them focus on its sum of delays. Different from traditional bifurcation analysis of Chua’s circuit system, the parameters are chosen as the bifurcation parameters in this paper such that the stability and bifurcation of the fractional-order Chua’s system is analyzed from a new angle. Then, the conditions of the existence for Hopf bifurcations are achieved by analyzing its characteristic equation. Finally, the validity and rationality of the theory are verified by numerical simulation.

[1]  Jeffrey B. Burl,et al.  A New Real-Time Optimal Energy Management Strategy for Parallel Hybrid Electric Vehicles , 2019, IEEE Transactions on Control Systems Technology.

[2]  Jing Zhang,et al.  A novel stability criterion of the time-lag fractional-order gene regulatory network system for stability analysis , 2019, Commun. Nonlinear Sci. Numer. Simul..

[3]  Dumitru Baleanu,et al.  Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations , 2017 .

[4]  Ozkan Guner.  Exp-Function Method and Fractional Complex Transform for Space-Time Fractional KP-BBM Equation , 2017 .

[5]  Hongxing Wang,et al.  Robust Adaptive Control for Fractional-order Financial Chaotic Systems with System Uncertainties and External Disturbances , 2017, Inf. Technol. Control..

[6]  J. A. Tenreiro Machado,et al.  Dynamic stability analysis of fractional order leaky integrator echo state neural networks , 2017, Commun. Nonlinear Sci. Numer. Simul..

[7]  Yong He,et al.  Stability analysis for impulsive fractional hybrid systems via variational Lyapunov method , 2017, Commun. Nonlinear Sci. Numer. Simul..

[8]  Adel Mellit,et al.  Control of chaos in an induction motor system with LMI predictive control and experimental circuit validation , 2017 .

[9]  Shen Yin,et al.  A New Disturbance Attenuation Control Scheme for Quadrotor Unmanned Aerial Vehicles , 2017, IEEE Transactions on Industrial Informatics.

[10]  H. Hassanabadi,et al.  Investigation of Conformable Fractional Schrödinger Equation in Presence of Killingbeck and Hyperbolic Potentials , 2017 .

[11]  Ronilson Rocha,et al.  Memristive oscillator based on Chua’s circuit: stability analysis and hidden dynamics , 2017 .

[12]  Guillermo Fernández-Anaya,et al.  Lyapunov functions for a class of nonlinear systems using Caputo derivative , 2017, Commun. Nonlinear Sci. Numer. Simul..

[13]  Ricardo Almeida,et al.  A Caputo fractional derivative of a function with respect to another function , 2016, Commun. Nonlinear Sci. Numer. Simul..

[14]  Bocheng Bao,et al.  Inductor-free simplified Chua’s circuit only using two-op-amp-based realization , 2016 .

[15]  Majid Yousefikhoshbakht,et al.  An Effective Rank Based Ant System Algorithm for Solving the Balanced Vehicle Routing Problem , 2016 .

[16]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[17]  Jacques Kengne,et al.  On the Dynamics of Chua’s oscillator with a smooth cubic nonlinearity: occurrence of multiple attractors , 2017 .

[18]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .