[PDF] Top 20 Chaos in a fractional order modified Duffing system

... study fractional order systems is through linear ...obtain a linear approximation for the fractional order integrator, the order of which depends on the desired bandwidth and the ... See full document

... is a 300-year-old mathematical topic [37–40]. Although it has a long history, the applications of fractional calculus to physics and engineering are just a recent focus of interest ...The ... See full document

... þ a_xðx 2  1Þ  b sin xt ¼ 0 ð4Þ In ...for a conservative harmonic force which determines the intrinsic oscillation ...During a complete cycle of oscillation, the energy is dissipated if ... See full document

... Abstract In this paper, chaos of a generalized van der Pol system with fractional orders is ...considered in detail. Chaos in the nonautonomous generalized van der ... See full document

... The chaos of the nonlinear damped Mathieu system and of the nano resonator system with its fractional order form Mechanical resonance is widely applied in high-precision ... See full document

... of chaos of fractional order modified van der Pol systems is ...of a constant term and addi- tion of kjxjsin x term where x is a state of the system are used to anticontrol the ... See full document

... follows. In Section 2, the review and the approximation of a fractional operator are ...given. In Section 3, the chaos in the autonomous fractional order rotational ... See full document

... Abstract In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are ...of a third nonautonomous or autono- mous ... See full document

... problems in real dynamical systems is actual asymptotical stability, although may not be mathe- matical asymptotical ...states in the neighborhood of zero solution must approach the origin as t ? ...only ... See full document

... chaotic system is nonlinear, the above “linear” controls [3,4,9–11] do not guarantee stability or performance in the global ...the system lies outside the attraction basin, the state trajectory will ... See full document

... Conclusions In this paper, a new strategy by using GYC partial region stability theory is proposed to achieve chaos ...is a simple linear homogeneous function of states and the lower ... See full document

... is a negative definite function in the first ...shown in Figs. 20 and 21. 5. Conclusions In this paper, a new strategy by using GYC partial region stability theory is proposed to achieve ... See full document

... Abstract Chaos synchronization by driving parameter for two uncoupled identical chaotic double Duffing systems is ...of a third chaotic system, the synchronization or anti-synchronization of two ... See full document

... presents a new hyperchaotic sys- tem with three positive Lyapunov exponents (called ...come a new four order system—Mathieu–van der Pol autonomous ...the system can present more ... See full document

... The chaos anti-control and synchronization of a two-degrees-of-freedom loudspeaker system are studied in this ...to chaos. The anti-control methods such as addition of a constant ... See full document

... Abstract Chaos and chaos synchronization of the horizontal platform system are studied in this ...and chaos synchronization are ...parameters in the system can be found ... See full document

... of a fractional delay filter into the one of a first-order differentiator such that the conventional finitie- impulse response and infinite-impulse response differentiators can be applied to ... See full document

... From variations of the phase portrait X versus X and/or the return map a state diagram which illustrates the thresholds of hysteresis jump, period doubling, and crisis in F versus co spa[r] ... See full document

... which in general cannot be ...linear system, the study of the types of periodic solution, the effects to the solutions caused by different para- meters and initial conditions and the stability analysis of ... See full document

... propagation in a random birefringent ®bre are ...soliton in- teractions in a polarization-division multiplexing transmission ... See full document