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Delay-induced multi-stability in Wilson-Cowan model with external input
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DOI：10.1007/s11071-026-12922-w.png)
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Abstract
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Based on the Wilson-Cowan model, this paper establishes a dynamical model for single- and two-population neural systems under both undelayed and delayed conditions, and systematically investigates the synergistic regulatory mechanisms of coupling strength, conduction delay, and external input. The results show that the system undergoes a Hopf bifurcation only under sustained external stimulation in the undelayed single-population system. In contrast, a millisecond-scale delay alone can independently induce oscillations, and increasing external input compensatorily lowers the critical delay threshold. In the asymmetric two-population system, a reduction in local gain causes bistability to degenerate into monostability via a saddle-node bifurcation, whereas gain modulation and external input can equivalently reshape the bistability. Under delayed conditions, time delay triggers instability through a saddle-node bifurcation of periodic orbits, directly generating oscillations. After external input is introduced, multiple bifurcation types, including Hopf bifurcation, emerge, progressively driving the system to transit from tristability to bistability and ultimately to global monostability. These findings provide a dynamical-level theoretical explanation for the generation of neural rhythms and for clinical neuromodulation.
Keywords:
Wilson-Cowan model
Stability
Time delay
Bifurcation
Asymmetric coupled populations
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6
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1.4W
Citations:
4.1W
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