Advanced Differential Equations and Dynamical Systems

New topologies in the unfolding of the Doubly DegenerateBogdanov-Takens bifurcation

This paper investigates the unfolding of the Doubly Degenerate Bogdanov-Takens bifurcation using spherical and planar surfaces, revealing new bifurcation topologies and transitions relevant to neural dynamics.

Existence and Localization of a Limit Cycle in a Class of Benchmark Biomolecular Oscillators

The paper proves the existence and localizes limit cycles in biomolecular oscillators using a geometric approach and interval-based reachability analysis.