Chaotically Spiking Canards in an Excitable System with 2D Inertial Fast Manifolds
نویسندگان
چکیده
منابع مشابه
Chaotically spiking canards in an excitable system with 2D inertial fast manifolds.
We introduce a new class of excitable systems with two-dimensional fast dynamics that includes inertia. A novel transition from excitability to relaxation oscillations is discovered where the usual Hopf bifurcation is followed by a cascade of period doubled and chaotic small excitable attractors and, as they grow, by a new type of canard explosion where a small chaotic background erratically bu...
متن کاملExcitable Neurons, Firing Threshold Manifolds and Canards
We investigate firing threshold manifolds in a mathematical model of an excitable neuron. The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to propofol anesthesia and is adapted from McCarthy et al. (SIAM J. Appl. Dyn. Syst. 11(4):1674-1697, 2012). Propofol modulates the decay time-scale of an inhibitory GABAa synaptic current. Interestingly, this system give...
متن کاملOn bifurcations in a chaotically stirred excitable medium
We study a one-dimensional filamental model of a chaotically stirred excitable medium. In a numerical simulation we systematically explore its rich bifurcation scenarios involving saddle-nodes, Hopf bifurcations and hysteresis loops. The bifurcations are described in terms of two parameters signifying the excitability of the reacting medium and the strength of the chaotic stirring, respectively...
متن کاملChaotically spiking attractors in suspended-mirror optical cavities.
A high-finesse suspended-mirror Fabry-Perot cavity is experimentally studied in a regime where radiation pressure and photothermal effect are both relevant. The competition between these phenomena, operating at different timescales, produces unobserved dynamical scenarios where an initial Hopf instability is followed by the birth of small-amplitude chaotic attractors that erratically but determ...
متن کاملSpontaneous secondary spiking in excitable cells.
Kepler & Marder (1993, Biol. Cybern.68, 209-214) proposed a model describing the electrical activity of a crab neuron in which a train of directly induced action potentials is sometimes followed by one or more spontaneous action potentials, referred to as spontaneous secondary spikes. We reduce their five-dimensional model to three dimensions in two different ways in order to gain insight into ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2007
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.98.074104