Geodesic
Spiral chaos in Lotka-Volterra like models
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 2, pp. 13-24

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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.
Mots-clés : spiral chaos
Keywords: Lotka-Volterra-like systems, strange attractor. 
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     title = {Spiral chaos in {Lotka-Volterra} like models},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
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Y. V. Bakhanova; A. O. Kazakov; A. G. Korotkov. Spiral chaos in Lotka-Volterra like models. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 2, pp. 13-24. http://geodesic.mathdoc.fr/item/SVMO_2017_19_2_a0/