Dynamics of three interacting species in single compartment and in spatially extended system by moment equations

Real ecosystems are influenced by random fluctuations of environmental parameters, such as temperature, food resources, migrations, genetic changes. This caused, during last decades, an increasing interest on the role played by the noise in population dynamics. In systems governed by nonlinear dynamics the presence of noise sources can give rise to counterintuitive phenomena like stochastic resonance, noise enhanced stability, resonant activation, noise delayed extinction. Therefore, the stability of biological systems in the presence of noise sources has become one of the most relevant topics both in experimental and theoretical investigations on complex systems. In this work we consider t…