| Abstract: |
| In this talk, we construct an inertial two-neuron system with non-monotonic activation function and illustrate the stable coexistence of many dynamical behaviors that arise via the different bifurcation routes. To this end, we firstly analyze the system equilibria by the nullcline curves. By the pitchfork/saddle-node bifurcation of the trivial/nontrivial equilibria, the system parameter plane of coupling weight is divided into the different regions having different number of equilibria. With coupling weight increasing, the system generates two coexisting single-scroll chaotic attractors via the period-doubling bifurcation. Further, the single-scroll chaos will evolve into the double-scroll chaotic attractor. Employing numerical simulations, we present many types of multistability, such as bistable periodic orbits, multistable periodic orbits, and multistable chaotic attractors. On the other hand, taking into consideration of coupling delay, the trivial and nontrivial equilibria lose their stability and bifurcate into periodic orbits. The system has the stable coexistence of two periodic orbits near the nontrivial equilibria. For some regions of coupling delay, the system illustrates the stability switching. Using the Hopf-Hopf bifurcation analysis, we find a quasi-periodic orbit surrounded by the trivial equilibrium. Further, the system presents multiple stable coexistence by the different bifurcation routes, i.e., the period-doubling and quasi-periodic bifurcations. |
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