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We are still far from a comprehensive theory of bifurcation in dynamical systems with multiple time scales. However, systematic application of geometric methods and study of examples have produced d...
Relaxation oscillations are periodic orbits of multiple time scale dynamical systems that contain both slow and fast segments. The slow-fast decomposition of these orbits is de ned in the singular l...
This paper presents a detailed analysis of mixed-mode oscillations in the “autocatalator,” a threedimensional, two time scale vector field that is a chemical reactor model satisfying the law of mass ...
A lattice model of three-state stochastic phase-coupled oscillators has been shown by Wood et al. [Phys. Rev. Lett. 96, 145701 (2006)] to exhibit a phase transition at a critical value of the coupling...
Alternating patterns of small and large amplitude oscillations occur in a wide variety of physical, chemical, biological and engineering systems. These mixed-mode oscillations (MMOs) are often found i...
We analyze a piecewise-linear FitzHugh-Nagumo model. The system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist. The addition of small noise induces mixed-m...
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different...
A characteristic feature of the Portevin - Le Chatelier effect or the jerky flow is the stick-slip nature of stress-strain curves which is believed to result from the negative strain rate dependence ...

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