Browsing by Author "Moroz, Dmytro M."

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    Homoclinic and Heteroclinic Neural Odes: Theory and Its Use to Construct New Chaotic Attractors
    (Oles Honchar Dnipro National Universuty, Dnipro, 2025) Belozyorov, Vasiliy Ye.; Moroz, Dmytro M.; Volkova, Svetlana A.
    ENG: 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.
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    On Chaotic Attractors Whose Basins of Attraction Coincide With the Whole Space
    (Oles Honchar Dnipro National University, 2025) Belozyorov, Vasiliy Ye.; Moroz, Dmytro M.; Volkova, Svetlana A.
    ENG: A new type of chaotic attractors, whose basin of attraction is the entire phase space, is considered. The main difference between these attractors and the known ones is that any trajectory starting from the basin of attraction first enters a unique transport channel (which is a straight line), and then the trajectory reaches the attractor itself along this channel. For any quadratic dynamic system generating the mentioned attractor, a new concept of a uniquely defined degenerate autonomous quadratic dynamic system with exactly one real double equilibrium point is introduced. It is shown that if the degenerate system exhibits chaotic behavior, then the original (non-degenerate) system also exhibits similar chaotic behavior.