Spatiotemporal complexity analysis of a discrete space-time cancer growth model with self-diffusion and cross-diffusion
Year: 2024
Type: article
Abstract: We investigate spatiotemporal pattern formation in cancer growth using discrete time and space variables. We first introduce the coupled map lattices (CMLs) model and provide a dynamical analysis of its fixed points along with stability results. We then offer parameter criteria for flip, Neimark–Sacker, and Turing bifurcations. In the presence of spatial diffusion, we find that stable homogeneous solutions can experience Turing instability under certain conditions. Numerical simulations reveal a variety of spatiotemporal patterns, including patches, spirals, and numerous other regular and irregular patterns. Compared to previous literature, our discrete model captures more complex and richer nonlinear dynamical behaviors, providing new insights into the formation of complex patterns in spatially extended discrete tumor models. These findings demonstrate the model’s ability to capture complex dynamics and offer valuable insights for understanding and treating cancer growth, highlighting its potential applications in biomedical research.
Authors: Ying Sun, Jinliang Wang, You Li, Yanhua Zhu, Haokun Tai, Xiangyi Ma
Institutions: Beihang University, Beijing Forestry University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $1,790
OpenAlex ID: W4402772971