Spiral chaos in Lotka-Volterra like models

In this work investigations are made of spiral chaos in generalized Lotka-Volterra systems and Rosenzweig-MacArthur systems that describe the interaction of three species. It is shown that in systems under study the spiral chaos appears in agreement with Shilnikov's scenario. When changing a parameter in the system a stable limiting cycle and a saddle-focus equilibrium are born from stable equilibrium. Then the unstable invariant manifold of saddle-focus winds on the stable limit cycle and forms a whirlpool. For some parameter's value the unstable invariant manifold touches one-dimensional stable invariant manifold and forms homoclinic trajectory to saddle-focus. If in this case the limiting cycle loses stability (for example, as result of sequence of period-doubling bifurcations) and saddle value of the saddle-focus is negative then strange attractor appears on base of homoclinic trajectory.