TY - JOUR

T1 - Homoclinic Chaos in a Kinetic Model of Heterogeneous Catalytic Reaction

AU - Chumakov, Gennadii A.

AU - Chumakova, Nataliya A.

N1 - Chumakov, G. A. Homoclinic Chaos in a Kinetic Model of Heterogeneous Catalytic Reaction / G. A. Chumakov, N. A. Chumakova // Computational Mathematics and Modeling. – 2026. – DOI 10.1007/s10598-026-09688-6. – EDN JVKVYE. The study was carried out within the framework of the State contracts of Sobolev Institute of Mathematics (project no. FWNF-2026-0026) and of Boreskov Institute of Catalysis (project no. FWUR 2024-0037).

PY - 2026/4/13

Y1 - 2026/4/13

N2 - This paper addresses the phenomenon of homoclinic chaos in a kinetic model with fast, intermediate, and slow variables. The model describes the dynamics of the heterogeneous catalytic reaction of interaction of hydrogen and oxygen on metallic catalyst. The subharmonic period-doubling cascade that is observed under a parameter variation in the system of three nonlinear ordinary differential equations leads to the generation of a global attractor. Using the Poincaré mapping and the second-iterate map, as well as their one-dimensional approximations, we prove the existence of a transversal homoclinic orbit to a saddle periodic Möbius orbit which generates the cascade of period-doubling bifurcations. The skeleton of the attractor consists of a family of unstable Möbius orbits of large periods. Numerical experiments show that a typical trajectory on the attractor under consideration is asymptotically chaotic.

AB - This paper addresses the phenomenon of homoclinic chaos in a kinetic model with fast, intermediate, and slow variables. The model describes the dynamics of the heterogeneous catalytic reaction of interaction of hydrogen and oxygen on metallic catalyst. The subharmonic period-doubling cascade that is observed under a parameter variation in the system of three nonlinear ordinary differential equations leads to the generation of a global attractor. Using the Poincaré mapping and the second-iterate map, as well as their one-dimensional approximations, we prove the existence of a transversal homoclinic orbit to a saddle periodic Möbius orbit which generates the cascade of period-doubling bifurcations. The skeleton of the attractor consists of a family of unstable Möbius orbits of large periods. Numerical experiments show that a typical trajectory on the attractor under consideration is asymptotically chaotic.

KW - Dynamical system

KW - Heterogeneous catalytic reaction

KW - Homoclinic chaos

KW - Kinetic model

KW - Möbius orbit

KW - Transversal homoclinic orbit

KW - Динамическая система

KW - Гомоклинический хаос

KW - Орбита Мёбиуса

KW - Трансверсальная гомоклиническая орбита

KW - Кинетическая модель

KW - Гетерогенная каталитическая реакция

UR - https://www.mendeley.com/catalogue/f6d889ec-45d6-3d92-9bdc-0d19167130a5/

UR - https://www.scopus.com/pages/publications/105035692927

UR - https://elibrary.ru/item.asp?id=90697645

U2 - 10.1007/s10598-026-09688-6

DO - 10.1007/s10598-026-09688-6

M3 - Article

VL - 37

SP - 183

EP - 196

JO - Computational Mathematics and Modeling

JF - Computational Mathematics and Modeling

SN - 1046-283X

IS - 1

ER -