Detecting Canard Tori in Quadratic Jerk Systems via Higher-Order Averaging Theory

Resumo

In this work, we develop a higher–order averaging approach, in the spirit of [1], to detect canard tori in a general quadratic jerk system. By combining classical averaging techniques with methods for the detection of torus bifurcations, we obtain a framework that we apply to a three–dimensional quadratic jerk system exhibiting a zero–Hopf equilibrium. In this context, the loss of stability of a periodic orbit leads to the emergence of a canard torus, which is rigorously detected as a Neimark–Sacker bifurcation in the corresponding Poincaré map. We provide a precise statement of the main result, together with a detailed computational scheme and numerical illustrations.