Higher order solitary solutions to the meta-model of diffusively coupled Lotka-Volterra systems

A meta-model of diffusively coupled Lotka-Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of nth order solitary solutions are derived via a modified inverse balancing technique. It is shown that as the highest possible solitary solution order n is increased, the number of nonzero solution parameter values remains constant for solitary solutions of order $n>3$ . Analytical and computational experiments are used to illustrate the obtained results.