We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3).

In this paper, we consider an autonomous Lotka-Volterra stochastic competitive system with feedback controls and infinite delays. Sufficient conditions which ensure the global stability of the system is considered. Some simulation figures are introduced to support the analytical findings.

Predictive microbiology is an emerging research domain in which biological and mathematical knowledge is combined to develop models for the prediction of microbial proliferation in foods. To provide accurate predictions, models must incorporate essential factors controlling microbial growth. Current models often take into account environmental conditions such as temperature, pH and water activi...

In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters. 1. The Periodic Lotka-Volterra System. Consider the Predator-Prey model (see Volterra [1]) N ′ 1 = (ε1 − γ1N2)N1 N ′ 2 = (−ε2 + γ2N1)N2. (1) The functions N1 and N2 measure the ...

By adding the concept of random embryology with locality to Lotka-Volterra population equations, a description of biological evolution is created. This model is called Ecolab. Computer simulations of these systems display self organised criticality, with power law behaviour for species lifetimes that stand in stark contrast to gradualism. This paper explores areas of future research with this m...