Structure of saddle-node and cusp bifurcations of periodic orbits near a non-transversal T-point

Non-transversal T-points have been recently found in problems from many different fields: electronic circuits, pendula, and laser problems. In this work, we study a model based on the construction of a Poincaré map that describes the behaviour of curves of saddle-node and cusp bifurcations in the vicinity of such a non-transversal T-point. This model is also able to predict, reproduce, and explain the numerical results previously obtained in Chua’s equation.

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