Feedback loops for chaos in activator-inhibitor systems

Abstract

Previous investigations have revealed that special constellations of feedback loops in a network can give rise to saddle-node and Hopf bifurcations and can induce particular bifurcation diagrams including the occurrence of various codimension-two points. To elucidate the role of feedback loops in the generation of more complex dynamics, a minimal prototype for these networks will be taken as purely periodic starting model which will be extended by an additional species in different feedback loops. The dynamics of the resulting systems will be analyzed numerically for the occurrence of chaotic attractors. Especially, the consequences of codimension-two bifurcations and the role of homoclinic orbits in view of the emergence of Shil'nikov chaos will be discussed.