Non Linear System for a Veritable PID Substitute

Non linear system Lotka Voltera described process of prey-predator evolution in nature. One of them is formulated in normal Cauchy form, as in the following form

where P is number of predators and H represent individs number in prey.

The grows rates are: r for H, a is the rate of predators, b is the rate for predators when one individ of prey is reated and c is the death rate in predators’ individs.

This system is very strong of nonlinearity represent, with constant coefficients becomes surprising with changes them values. The system was integrated by numerical method Runge Kutta or Euler II for any coefficient’s values.