Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors - Vasiliy Ye. Belozyorov; Dmytro M. Moroz; Svetlana A. Volkova (Journal of Optimization, Differential Equations and Their Applications)
New types of neural ordinary differential equations (NODE) with power nonlinearities are considered. For these NODE systems, new conditions for the existence of homoclinic and heteroclinic orbits are found. In the future, the implementation of these conditions guarantees the existence of chaotic attractors in the mentioned NODE systems.