Chaos and optimal control of cancer self-remission and tumor system steady states

This paper is devoted to study the problem of optimal control of cancer self-remission and tumor unstable steady-states. The stability analysis of the biologically feasible equilibrium states is presented using a local stability approach. The system appears exhibit a chaotic behavior for some ranges of the system parameters. The necessary optimal control inputs for the asymptotic stability of the positive equilibrium states and minimizes the require performance measure are obtained as nonlinear function of the system densities. Analysis and extensive numerical examples of the uncontrolled and controlled systems were carried out for various parameters values and different initial densities.