Mathematics of Nerve Signals

Peets, Tanel; Tamm, Kert

doi:10.1007/978-3-030-29951-4_10

Cited by 6 publications

(8 citation statements)

References 65 publications

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“…These findings are supported by detailed mathematical modelling and computational simulations [62][63][64][65][66][67][68][69] Table 1 -The Action Potential Pulse (APPulse) -there is accumulating evidence for the soliton pressure pulse in neuronal membranes.…”

mentioning

confidence: 86%

Nerve Impulses Have Three Interdependent Functions: Communication, Modulation, and Computation

Winlow

Johnson

2021

Bioelectricity

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mentioning

confidence: 86%

Nerve Impulses Have Three Interdependent Functions: Communication, Modulation, and Computation

Winlow

Johnson

2021

Bioelectricity

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“…Herein we follow the ideas of modelling proposed by Engelbrecht, Tamm and Peets in their recent publications [16,[18][19][20][21][22][23][24], see also [44]. The modelling is based on the careful analysis of the mechanisms of electro-mechanophysiological interactions (see summary in [23,24]).…”

Section: Mathematical Modelling Of Signal Components In Nervesmentioning

confidence: 99%

Signals in nerves from the philosophical viewpoint

Engelbrecht¹,

Tamm²,

Peets³

2022

PEAS

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Signals in nerves include electrical, mechanical and thermal components and are characterised by the complexity of processes. The modelling of these signals is analysed from the viewpoint of DeLanda, who has demonstrated the possibility of revealing Deleuze's philosophical theories by using the notions from nonlinear dynamics. It is shown that the mathematical modelling of processes in nerves by the authors of this paper follows the general ideas of multiplicity and causal interactions described by DeLanda.

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“…Proof. Equality (15) follows easy from ( 7) and (14). We study the spectrum of the operator F , linearized around ϕ c .…”

Section: Let Us Consider the Operatorsmentioning

confidence: 99%

“…For more details about the discussed models, see in [9,10,12,13] and the references therein. Recently in [14] the authors propose a joint coupled model, which is able to describe the electric, mechanical and thermal effects of propagation of axons. In this model, an additional coupling force is included in Equation (1).…”

Section: Introductionmentioning

confidence: 99%

Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

2021

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We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity f(u)=a|u|pu+b|u|2pu,p>0,a∈R,b∈R,b≠0. The stability of solitary waves with velocity c, c2<1 is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function d(c), related to some conservation laws. We derive explicit analytical formulas for the function d(c) and its second derivative for quadratic-cubic nonlinearity f(u)=au2+bu3 and parameters b>0, c2∈0,min1,h1h2. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity f(u)=bu3.

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Mathematics of Nerve Signals

Cited by 6 publications

References 65 publications

Nerve Impulses Have Three Interdependent Functions: Communication, Modulation, and Computation

Nerve Impulses Have Three Interdependent Functions: Communication, Modulation, and Computation

Signals in nerves from the philosophical viewpoint

Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

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