Awakened Oscillations in Coupled Consumer-Resource Pairs
Figure 5
(a) Phase plane of the slow subsystem (43a)–(43d) sectored (by dashed lines) into stability domains of the corresponding quasi-steady states of the fast subsystem (42a)–(42c). Both boundary quasi-steady states, each corresponding to the situation when either of the two consumers completely dominates, are stable within the opening of the angle formed by the dashed lines. Lines and are the respective nullclines and of the piecewise subsystem (47a)-(47b). Lines and mean the same for the piecewise subsystem (52a)-(52b). Intersections of the nullclines (marked by the open circles) are equilibria of the associated piecewise slow subsystems, and they must lie outside the above-mentioned opening to allow for the relaxation oscillations. (b), (c), and (d) are the respective phase portraits of the fast subsystem (42a)–(42c) generated by points “b,” “c,” and “d” in the slow phase plane (a).
