Chaos and multistability behaviors in 4D dissipative cancer growth/decay model with unstable line of equilibria

Abstract

The objective of this paper is to study the chaos and multistability behaviors in a 4D dissipative chaotic cancer growth/decay model. The 4D chaotic cancer growth/decay model has chaotic 2-torus and 2-torus quasi-periodic unique behaviors which reflect the fact that the tumor cell density has 2-torus quasi-periodic bifurcation between two values. As the tumor cell production rate is increasing, the bifurcation is growing more rapidly as chaotic 2-torus evolution and the tumor cell density becomes unstable. The 4D cancer growth/decay model has an unstable line of equilibria with saddle-focus behavior. The chaos and multistability behaviors are explored with different qualitative and quantitative dynamic tools like Lyapunov exponents, Lyapunov dimension, bifurcation diagram and Poincaré map. Tumor cell escalation/de-escalation, glucose level, number of tumor cells are considered to analyses chaos and multistability behaviors. The existence of multistability behavior in the 4D cancer model reveals that the different phenotypes are adopted by tumor cells, some of them become metastatic, adopt different behaviors and turn into a genomic event. The multistability behavior in the 4D chaotic cancer growth/decay model may be of capital importance in the dynamic evolution of the tumor since complication may occurs even after the required therapy. Simulations are done in MATLAB environment and are presented for effective verification of numerical approach. MATLAB simulated results correspond successful achievement of the objective.