Pattern formation and parameter inversion for a discrete Lotka–Volterra cooperative system

Highlights: • Turing instability condition for a discrete cooperative model is deduced. • Interesting patterns such as spiral wave, chaos are selectively obtained. • A Newton method is applied to parameter inversion. • Numerical simulation can verify the effectiveness of the regularization method. - Abstract: In this paper, stability analysis is applied to a discrete Lotka–Volterra cooperative system with the periodic boundary conditions, then Turing pattern formation conditions can be derived, theory analysis and numerical simulation show that turing patterns can be realized. In addition, we also pay attention on what reason or what system environment to result into the current state patterns, which can be reduced to estimate or identify the system parameter. A regularization method is applied to parameter inversion, and numerical simulation can verify the effectiveness of the algorithm.