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A Geometric Model for Mixed-Mode Oscillations in a Chemical System
mixed-mode oscillations bifurcations kneading theory
2015/8/25
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
...
Global return maps for mixed-mode oscillations with one fast and two slow variables
Dynamical Systems (math.DS) Classical Analysis and ODEs (math.CA) Chaotic Dynamics (nlin.CD)
2010/11/10
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...
Mixed-Mode Oscillations in a Stochastic, Piecewise-Linear System
Dynamical Systems (math.DS) Chaotic Dynamics (nlin.CD)
2010/11/10
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...
Characterizing mixed mode oscillations shaped by noise and bifurcation structure
mixed mode oscillations underlying dynamical structure extrinsic noise
2010/4/2
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...