On the nonexistence of periodic orbits and instability in nonlinear fourth-order multi-delay vector systems

Sultan Erdur; Sultan Erdur

doi:10.3934/math.2026966

AIMS Mathematics

2026, Volume 11, Issue 8: 23979-23994. doi: 10.3934/math.2026966

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On the nonexistence of periodic orbits and instability in nonlinear fourth-order multi-delay vector systems

Sultan Erdur ^,

Department of Mathematics, Faculty of Art and Science, Gaziantep University, Gaziantep, 27310, Turkey

Received: 01 March 2026 Revised: 30 June 2026 Accepted: 27 July 2026 Published: 05 August 2026
MSC : 34K20, 34D20

This study establishes a new set of sufficient criteria for guaranteeing the nonexistence of nontrivial periodic solutions and the instability of the trivial solution for a class of nonlinear fourth-order vector differential equations with multiple delays by constructing an appropriate Lyapunov–Krasovskii (LK) functional specifically tailored to the system's dynamics. The proposed approach provides a consistent basis that supports and builds on findings in the literature by incorporating multiple delay terms in a vector structure. Furthermore, two examples illustrate the applicability of the theoretical results. These findings provide a robust basis for the analyses of nonexistence and instability of higher-order systems in engineering and applied mathematics.
Citation: Sultan Erdur. On the nonexistence of periodic orbits and instability in nonlinear fourth-order multi-delay vector systems[J]. AIMS Mathematics, 2026, 11(8): 23979-23994. doi: 10.3934/math.2026966

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Abstract

This study establishes a new set of sufficient criteria for guaranteeing the nonexistence of nontrivial periodic solutions and the instability of the trivial solution for a class of nonlinear fourth-order vector differential equations with multiple delays by constructing an appropriate Lyapunov–Krasovskii (LK) functional specifically tailored to the system's dynamics. The proposed approach provides a consistent basis that supports and builds on findings in the literature by incorporating multiple delay terms in a vector structure. Furthermore, two examples illustrate the applicability of the theoretical results. These findings provide a robust basis for the analyses of nonexistence and instability of higher-order systems in engineering and applied mathematics.

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