Chaotic Attractor in Tumor Growth and Decay A Differential Equation Model

Cancer growth and decay can be modeled as a system of chaotic nonlinear differential equations. The system is based on a reaction-diffusion cancer growth model, expressed by: The above model will be simplified by Ivancevicet. al (eqs. 12 – 15) so as to allow useful parameters to be applied for simulation and then recreated in C/Java, to directly compare with its predecessor project created by Ivancevicet. al (simulated in Wolfram CDF and Mathematica). Varying input parameters of glucose and oxygen levels will be examined to determine chaos behavior. Ultimately, the result is the development of a bifurcation graph to characterize chaotic behavior. Based on this result, the model parameters will be optimized in order to minimize chaos in the system. Methodology From the reaction-diffusion cancer growth model above, a simplified non-dimensional non-spatial derivative model was found.This model was further modified by adding four additional parameters (α, β, γ, δ) which represents tumor cell volume, glucose level, number of tumor cells, and diffusion saturation level from the surface, respectively. The starting point of the generation C/Java simulations is expressed by