Bifurcation Near a Transcritical Singularity in Planar Singularly Perturbed Systems
Copyright policy )Bifurcation Near a Transcritical Singularity in Planar Singularly Perturbed Systems
ABSTRACTWe classify all bifurcation phenomena of the flow near a transcritical singularity in planar singularly perturbed differential systems that do not have a breaking parameter via qualitative analysis and blow‐up technique. Here, the directional blown up vector fields can have several singularities and no first integral that are different from those in the literatures. The obtained local bifurcations are also illustrated by numerical simulations through a modified Leslie–Gower model, whose global dynamics is thereby obtained.
- Nanchang Normal University China (People's Republic of)
- Shanghai Jiao Tong University China (People's Republic of)
- Fujian Normal University China (People's Republic of)
Bifurcation theory for ordinary differential equations, Singular perturbations for ordinary differential equations, blow-up technique, geometric singular perturbation theory, transcritical singularity, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, breaking parameter
Bifurcation theory for ordinary differential equations, Singular perturbations for ordinary differential equations, blow-up technique, geometric singular perturbation theory, transcritical singularity, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, breaking parameter
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