Bifurcation of homoclinics in a nonlinear oscillation

Zhang, Weinian

doi:10.1007/bf02107670

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+ G(x) = −λ ẋ + µ[Cos T + F (T)]1

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2021

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Cited by 6 publications

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“…In fact, they obtained some regions divided by some submanifolds with codimension one near zero in infinite-dimensional spaces where there were either the existence of homoclinics (subharmonics) or the nonexistence for the perturbed system. This work was generalized by He and Zhang [15,17].…”

Section: + G(x) = −λ ẋ + µ[Cos T + F (T)]mentioning

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: + G(x) = −λ ẋ + µ[Cos T + F (T)]mentioning

confidence: 99%