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This paper proposes a novel jerk circuit obtained by using an alternative nonlinear bipole component of inductor and diode in parallel. The circuit is described by five differential equations and investigated by the stability analysis, equilibria points, Kaplan–Yorke dimension, phase portraits, Lyapunov characteristic exponent estimation, bifurcation diagram and the 0–1 test chaos detection. The control parameter is adopted by varying the inductor L value, this system can display periodic orbit, quasi-periodic orbit and chaotic behavior. The dynamic influence of transit diode capacitance is done and this confirms the robustness of the system to noise influence. The validity of the numerical simulations is experimentally realized through the phase portraits of the circuit. Finally, the synchronization of the systems is studied and time simulation results are presented. [ABSTRACT FROM AUTHOR]

By diode bridging an inductor to implement a memristor bipole, with active Wien-bridge oscillator, a simple and feasible third-order autonomous memristive chaotic oscillator is presented. The dynamical characteristics of the proposed circuit are investigated both theoretically and numerically, from which it can be found that the circuit has one unstable equilibrium point. Through the analysis of the bifurcation diagram, Lyapunov exponent spectrum and the 0–1 test chaos detection, it is shown that this system displays limit cycle orbit with different periodicity, quasi-periodic behavior, chaotic behavior and bursting behavior. The bursting behavior found in this circuit is periodic, quasi-periodic and chaotic bursting. We confirm the feasibility of the proposed theoretical model using Pspice simulations and a physical realization based on an electronic analog implementation of the model. [ABSTRACT FROM AUTHOR]

This work presents the determination of Lyapunov spectrum of fractional order dynamical systems. The method considers the Cloned Dynamic technique, which is based on time evaluation of exact copies of dynamic equations with small initial conditions disturbances. As its calculations are simple, this method can be applied to various dynamic systems types, in particular fractional order, nonlinear and time varying systems, and non linear systems where Jacobian are impossible to evaluate. The predictor-corrector Adams-Bashforth-Moulton algorithm is used for fractional order system numerical evaluation. All Lyapunov exponents are estimated based on the convergence or divergence of the small disturbed clones with respect to the reference (fiducial) trajectory and application of Gram-Schmidt Reorthonormalization after each convenient periodic time interval. To evaluate the application of this method, three third order dynamical systems are explored: Jerk, Financial, and a Four Wing systems. Integer order, commensurate fractional order and incommensurate fractional order are explored. To confirm chaotic or non-chaotic behavior, 0-1 Test is used and Jerk system is studied with a classical method for Lyapunov exponents determination also. The advantages and contribution of the proposed method the possibility to study incommensurate orders fractional cases and explore non linear systems without need of Jacobian determination, as is proved with applications shown. The Lyapunov Exponents and the phase portraits were simulated together to validate this method and the obtained results are in good agreement. [ABSTRACT FROM AUTHOR]