Continuous dynamical systems approach to analyzing quadratic stochastic operators

This paper investigates the behavior of quadratic stochastic operators using continuous dynamical systems. The Euler method is applied to convert a discrete system into a continuous one, and numerical methods are used to solve the resulting differential equations. The operator is defined in a two-dimensional simplex and the dynamics are analyzed by dividing the simplex into six regions. The results show that the dynamic of the operator is dependent on the value of a specific parameter. The use of continuous dynamical systems is shown to be an effective method for understanding the behavior of quadratic stochastic operators.