Darboux integrability of a new four-dimensional hyper-chaotic system

Muhsin Tahsin Najmadin; Niazy Hady  Hussein

doi:10.5269/bspm.80947

Muhsin Tahsin Najmadin Soran Univeristy
Niazy Hady Hussein Salahaddin Univeristy-Erbil

Abstract

This study addresses the Darboux integrability of a newly developed four-dimensional hyperchaotic system. Systems of this type are of considerable interest in the study of nonlinear dynamics due to their high-dimensional complexity and potential applications in secure communications, control theory, and cryptography. In this work, the proposed system is examined from the perspective of Darboux theory of integrability to identify its algebraic and analytic structures. The analysis indicates that the system lacks invariant algebraic surfaces and has only one Darboux element, which is an exponential factor. These results demonstrate that the system is non-integrable in the Darboux sense. Furthermore, it is demonstrated that under certain parameter constraints, the system fails to admit polynomial or rational first integrals.

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