Impulses and Physiological States in Theoretical Models of Nerve Membrane.

By R. FitzHugh. 1961

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Deep learning in neural networks: An overview (2014, background): “Current GPUs, however, are little ovens, much hungrier for energy than biological brains, whose neurons efficiently communicate by brief spikes (FitzHugh, 1961; Hodgkin & Huxley, 1952; Nagumo, Arimoto, & Yoshizawa, 1962), and often remain quiet.”
Physics-informed learning of governing equations from scarce data (2020, unknown): “SINDy has drawn tremendous attention in the past few years, leading to variant algorithms with applications to identify projected low-dimensional surrogate models in the form of first-order ODEs, alternatively with linear embedding [8, 10], for a wide range of nonlinear dynamical systems, such as fl”
Dynamic coordination between robots: self-organized timing selection in a juggling-like ball-passing task (2006, methodology): “A BVP (or FitzHugh–Nagumo) oscillator is a simple neural model with two variables, and it is known that this model is the qualitative equivalent of the Hodgkin–Huxley (H–H) neuron model, which expresses the response of an actual neuron well [ 12 ], [13].”
A pseudospectral method of solution of Fisher's equation (2006, methodology): “reaction–diffusion equation, will play an important role in the application of pseudospectral methods to more complex physical systems such as the Fitzhugh–Nagumo equation [20,37].”
Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs (2011, background): “Several examples are [1,2] from the gas dynamics, [3] from neurology, [4,5] from chemical engineering, [6–8] from the theory of solitons, [9,10] from the biology, [11–14] from theory of dynamical systems, chaos theory and ecology, and [15–20] from hydrodynamics and theory of turbulence.”
Existence and stability of traveling pulse solutions of the FitzHugh–Nagumo equation (2015, background): “Here w1(x, t) is the voltage inside the axon at position x ∈ R and time t.”
Excitability in ramped systems: the compost-bomb instability (2011, background): “(b) The return mechanism The most commonly studied return mechanism is found in variants of the excitable van der Pol and FitzHugh–Nagumo equations (van der Pol 1920; FitzHugh 1961; Nagumo et al. 1962; Doi et al. 1999; Izhikevich 2006) and can be modelled using excitable systems of the form: dx dt =”
Nonlinear dynamics of networks: the groupoid formalism (2006, methodology): “To provide a concrete example of dynamics in a symmetric network , we consider a specific system of ODEs determined by the two-cell network of Figure 1, based on the FitzHugh-Nagumo model of a neuron (FitzHugh [28], Nagumo et al. [61]).”
On partial contraction analysis for coupled nonlinear oscillators (2004, methodology): “…− 1, we are able to generate the tripod gait, a common hexapodal gait in which the front and rear legs on one side, and the middle leg on the other, move together, followed by the remaining Example 4.4 The FitzHugh–Nagumo (FN) model (FitzHugh1961; Nagumoetal.1962)isawell-knownspik-ing-neuronmodel.”