A meshless numerical method for a system with intraspecific and interspecific competition

In this paper we study a novel mathematical model with intraspecific and interspecific competition between two species consisting of non-linear parabolic–ODE–parabolic system. It describes the evolution populations in for resource, one which is subject to chemotaxis. We analyze local stability constant equilibrium solutions obtain periodic behavior solution certain data problem. For purpose, apply meshless numerical method Generalized Finite Differences (GFDM) prove conditional convergence discrete analytical one. The demonstrated and, thought its implementation, whose asymptotic agrees analytically expected. give several examples on applications over regularly irregularly distributed nodes illustrate potential.