Melnikov function and Poincaré map
Copyright policy )Melnikov function and Poincaré map
The following ODE is investigated: \(x''+g(x)=\epsilon \mu f(x,x')+\epsilon \delta h(x,x',\omega t)\) where \(h(x,x',\omega t)\) is periodic in t. A relationship between the Melnikov function and the Poincaré mapping is established and a new proof for the Melnikov method is given. Some illustrative examples are also presented.
- Beijing University of Technology China (People's Republic of)
Bifurcation theory for ordinary differential equations, Local and nonlocal bifurcation theory for dynamical systems, bifurcation, Melnikov method, Poincaré mapping, Asymptotic properties of solutions to ordinary differential equations
Bifurcation theory for ordinary differential equations, Local and nonlocal bifurcation theory for dynamical systems, bifurcation, Melnikov method, Poincaré mapping, Asymptotic properties of solutions to ordinary differential equations
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