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| The Dynamics of the Spruce Budworm-Bird System on Time Scale |
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| KeyWord:Slow-fast timescale, relaxation oscillation, canard cycle, predator-prey system |
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| Abstract: |
| We perform a geometric analysis focusing on relaxation oscillations and canard cycles within a singularly perturbed predator-prey system involving budworm and birds. The system undergoes a comprehensive stability analysis, leading to the identification of canard cycles in proximity to the Hopf bifurcation points. The study particularly highlights the transition from smaller Hopf-type cycles to larger relaxation cycles. And the expression of transition threshold $\mu _c(\sqrt{\varepsilon })$ of the spruce budworm-bird system is obtained innovatively. Furthermore, numerical simulations are carried out to validate the theoretical findings. |
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