The Mechanism of Chaotic Complexity in High‐Dimensional Linear Third‐Order Partial Differential Equation

This paper explores the chaotic behavior of both homogeneous and non‐homogeneous systems governed by linear third‐order partial differential equations on . Utilizing spectral properties of the semigroup generator, sufficient conditions for the relationship between the system coefficients and the occurrence of chaos have been established. These conditions can be effectively applied to examine chaos in Moore‐Gibson‐Thompson, linearized Westervelt, and linearized Kuznetsov equations. Furthermore, criteria for evaluating the stability are also formulated. Combining the criteria for stability and the occurrence of chaos, we have derived two necessary and sufficient conditions for the existence of chaos.