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Slow-fast cycles with points of self-intersections
No full textFor a class of slow-fast systems in the form ̇ =((,)−), ̇ =(,,) for (,,)∈ℝ× ℝ×ℝ, we study the cyclicity of slow-fast cycles with a more degenerate point of self-intersection and a generic contact point. By using entry-exit functions and slow divergence integrals, we show that the cyclicity of slow-fast cycles with points of self-intersection is at most one under some non-degenerate conditions for ≥1. Finally, we apply our theory to the classical Holling-Tanner model.Funding
Research of J.H. was partially supported by the National Natural Science Foundation of China (No. 12471162, 12231008).
Acknowledgements
The authors would like to thank Prof. Hao Wang, Prof. Shuang Chen, the editor and the reviewers for their helpful comments and suggestions on this work
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