| Abstract: |
| This talk introduces bifurcation scenarios in nonautonomous scalar ordinary differential equations whose derivative with respect to the state variable is concave in measure (so-called d-concave equations). Leveraging the strong constraints that d-concavity imposes on the global dynamics, we describe bifurcation patterns that, to the best of our knowledge, have not been reported previously. In particular, using a minimal but multiply ergodic skewproduct base, we construct an example of a jump bifurcation in which two nonhyperbolic compact invariant sets coexist, and each one disappears abruptly under parameter variation--one for each of the two possible directions of change. The study of such phenomena is motivated by critical transition theory, where small perturbations in the inputs of a complex system can trigger sudden and often irreversible shifts in its response. The nonautonomous bifurcations presented here provide a potential mechanism for critical transitions distinct from the better-studied saddle-node bifurcations. |
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