Evolutive Strategy to Inducing Chaos in a Gene Regulatory Network

In the present paper we propose an Evolutionary Strategy of Multiobjective Optimization like an alternative method to induce chaotic dynamics in a genetic regulatory network, called V-System, which was created by joining two systems of equations: one oscillating and one with a hysteresis dynamics. The genetic regulatory network is represented by four differential equations with seventeen parameters, which variables show the proteins concentrations. The multiobjective fitness function is built like a linear combination, involving a numerical approximation to Lyapunov exponents in the system, which is only dependent of the parameters fixed values. The optimization problem optimum represents the set of parameters values where the system is more chaotic. We present the numerical results of the evolutionary strategy and we show the convergence of the individuals in the population to the critical points in one of the subsystems in the V-System.