Basins of Attraction and Asymptotic Behavior of a Symmetric Feedback Loop Network with Parameter Heterogeneities

Many biological and physical (i.e. electronic) systems are known to oscillate only when they are driven by an external force. However, when they are connected in some fashion, the symmetry of the resulting topology of connections, i.e. which units are coupled with each other, and the nonlinear characteristics of each individual unit, can be exploited to generate self-sustained oscillations. One such type of network is a cyclic feedback loop, where each node is connected to the successor nodes in a cycle. In this work, we study the basins of attraction and the asymptotic behavior of a cyclic feedback loop, which has served as a model for the design and operation of sensor devices. Each node in the network exhibits bistability.