Turing instability and spatio-temporal pattern formation in a cancer growth model with diffusion and predator-taxis

In this study, we investigate a mathematical model for tumor growth that incorporates predator-taxis dynamics, focusing on the formation of spatial patterns and bifurcation behavior. A continuous reaction-diffusion system is studied with specific attention to the Turing instability and pattern selection mechanisms. By analyzing the stability of the homogeneous steady states and employing bifurcation theory, we establish conditions for Turing bifurcations. The dynamics of the model are explored in both the deterministic and stochastic regimes, with the latter incorporating Gaussian white noise to model inherent biological uncertainties. The influence of noise on stability is examined, revealing its role in enhancing the system’s robustness. Numerical simulations validate the theoretical results, and interesting Hopf-Turing patterns are observed within the Hopf bifurcation region. The interplay between tumor cell growth and predator-taxis is explored, providing insight into the spatial dynamics of tumor progression. This research contributes to the understanding of tumor growth mechanisms and opens avenues for developing new strategies for cancer therapy and treatment planning.