Dynamic Properties and Chaotic Phenomena in Concatenation Model with Power-law Nonlinearity with External Perturbation Terms

This paper presents an in-depth study of a concatenation model with power-law nonlinearity. The integral form of the original model is derived, and the corresponding dynamic system is obtained. A qualitative analysis is conducted to identify the types of equilibrium points, phase diagrams, and trajectories. From specific trajectories, we can infer that this equation has periodic and soliton solutions. To validate these conclusions, the corresponding exact solutions are constructed, and several new solutions are initially presented in this paper. Finally, by adding a specific external perturbation term, we found that this model also exhibits chaotic behavior, which is presented in this paper for the first time. Abstract Published by the Jagiellonian University 2025 authors