Perturbation of homoclinics and subharmonics in duffing's equation

Hale, Jack K.; Spezamiglio, Adalberto

doi:10.1016/0362-546x(85)90071-9

Cited by 14 publications

(2 citation statements)

References 3 publications

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“…They got some regions in the parameter spaces near zero where there were either homoclinic (subharmonic) solutions or no homoclinics (subharmonics) for the perturbed system. In 1985, Hale and Spezamiglio [9] studied the bifurcations of homoclinics and subharmonics of Duffing's equation ẍ − x + 2x 3…”

Section: Introductionmentioning

confidence: 99%

The coexistence of subharmonics bifurcated from homoclinic orbits in singular systems

Zhu

2008

Nonlinearity

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The bifurcations from degenerate homoclinics to linearly independent subharmonic solutions are considered for singular ordinary differential equations. The scalar ∈ R + and time-dependent function g are regarded as parameters. By means of the functional analytic method based on the Lyapunov-Schmidt reduction, we obtain various bifurcation functions where the zeros correspond to the various coexistences of subharmonic solutions at nonzero parameter values. These situations of various coexistences actually define different bifurcation manifolds with finite codimension in an appropriate parameter space.

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Section: Introductionmentioning

confidence: 99%

The coexistence of subharmonics bifurcated from homoclinic orbits in singular systems

Zhu

2008

Nonlinearity

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“…Harmonic solutions were investigated by McCartin using the method of van der Pol [17]. The behavior of the solutions of the Duffing equation near the separatrix were treated by Hale and Spezamiglio [34].…”

Section: Introductionmentioning

confidence: 99%

A qualitative study of the damped duffing equation and applications

Feng¹,

Chen²,

Hsu³

2006

Discrete &Amp; Continuous Dynamical Systems - B

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Abstract.In this paper, we analyze the damped Duffing equation by means of qualitative theory of planar systems. Under certain parametric choices, the global structure in the Poincaré phase plane of an equivalent two-dimensional autonomous system is plotted. Exact solutions are obtained by using the Lie symmetry and the coordinate transformation method, respectively. Applications of the second approach to some nonlinear evolution equations such as the twodimensional dissipative Klein-Gordon equation are illustrated.

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Bifurcation of homoclinics in a nonlinear oscillation

Zhang

1989

Acta Mathematica Sinica

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Perturbation of homoclinics and subharmonics in duffing's equation

Cited by 14 publications

References 3 publications

The coexistence of subharmonics bifurcated from homoclinic orbits in singular systems

The coexistence of subharmonics bifurcated from homoclinic orbits in singular systems

A qualitative study of the damped duffing equation and applications

Bifurcation of homoclinics in a nonlinear oscillation

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