منابع مشابه
Nonresonant Excitation of the Forced Duffing Equation
We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...
متن کاملBifurcations and Chaos in the Duffing Equation with One Degenerate Saddle Point and Single External Forcing
In this paper, we study the Duffing equation with one degenerate saddle point and one external forcing and obtain the criteria of chaos of Duffing equation under periodic perturbation through Melnikov method. Numerical simulations not only show the correctness of the theoretical analysis but also exhibit the more new complex dynamical behaviors, including homoclinic bifurcation, bifurcation dia...
متن کاملA Shooting Approach to Layers and Chaos in a Forced Duffing Equation
1 abstract We study equilibrium solutions for the problem u t = ε 2 u xx − u 3 + λu + cos x u x (0, t) = u x (1, t) = 0. Using a shooting method we find solutions for all non-zero ε. For small ε we add to the solutions found by previous authors, especially Angennent, Mallet-Paret and Peletier, and by Hale and Sakamoto, and also give new elementary ode proofs of their results. Among the new resu...
متن کاملFrequency–driven chaos in the electrical circuit of Duffing-Holmes oscillator and its control
Accurate detection of weak periodic signals within noise and possibility of secure messaging have made Duffing oscillator (DO) highly important in the field of communication. Investigation on the properties of DO is thus ardently sought for. An elegant approach to accomplish the same is to fabricate electronic circuit simulating DO non-linear equation and to study the effect of input signal amp...
متن کاملOn Lyapunov Control of the Duffing Equation
This brief addresses the robust asymptotic and BIB0(bounded-input bounded-output) stability of a class of linear shift-variant multidimensional systems. Using a shift-invariant comparisonsystem, necessary and sufficient conditions for the stability of the entirefamily of systems are derived.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1993
ISSN: 0022-0396
DOI: 10.1006/jdeq.1993.1013