Migration-connected networks of Lotka–Volterra and quasi-polynomial systems: modeling and decentralized control

This paper introduces a modeling and a control approach for Lotka-Volterra systems that are interconnected through population size-dependent migration flows. First, a control-oriented model is proposed for networks of Lotka-Volterra systems. Based on this model, a decentralized control method is introduced which assures that the states of each Lotka-Volterra system in the network can be driven into a prescribed setpoint regardless of migration. The results have been generalized to quasi-polynomial systems, and networks of Lotka-Volterra systems having interconnections with distributed delay. Simulation experiments are also presented in the paper to show the implementability of the theoretical results.