Constructing continuous multi-behavioral planar systems through motivation dynamics and bifurcations

This paper offers new analytical conditions on the system parameters of a particular class of planar dynamical systems which would allow them to undergo a Hopf bifurcation. These systems are constructed as a means of generating multiple behaviors from the same single continuous dynamical system model, without resorting to switching between distinct component continuous dynamics associated to each behavioral mode. This work builds on recent advances which introduced motivation dynamics as an efficient way to design multi-behavioral systems. The contribution of this paper is that it expands the scope of the motivation dynamics approach, and offers explicit analytic conditions on the system parameters to guarantee the existence of bifurcations, which can then be utilized to better engineer the structure and location of the resulting equilibria. Numerical simulations confirm the theoretical predictions for the onset of the Hopf bifurcations.