Application of differential equations with variable delay in the compartmental models of living systems

2021 ◽  
Vol 24 (3) ◽  
pp. 55-73
Author(s):  
N. V. Pertsev
Keyword(s):  
Differential Equations ◽  
Compartmental Models ◽  
Living Systems ◽  
Variable Delay

scholarly journals Lucas Polynomial solution of Nonlinear Differential Equations with Variable Delay

2019 ◽  
pp. 1-12 ◽  
Author(s):  
Sevin Gümgüm ◽  
Nurcan Baykuş Savaşaneril ◽  
Ömür Kıvanç Kürkçü ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Polynomial Solution ◽  
Variable Delay

Calibrating compartmental models of neurons

1978 ◽  
Vol 235 (1) ◽  
pp. R93-R98 ◽  
Author(s):  
D. H. Perkel ◽  
B. Mulloney
Keyword(s):  
Steady State ◽  
Electrical Properties ◽  
Differential Equations ◽  
Compartmental Model ◽  
Compartmental Models ◽  
Electrical Measurements ◽  
Original Matrix ◽  
Systematic Procedure ◽  
The Matrix ◽  
Voltage Attenuation

Numerical parameters for a compartmental model of a neuron can be chosen to conform both to the neuron's structure and to its measured steady-state electrical properties. A systematic procedure for assigning parameters is described that makes use of the matrix of coefficients of the set of differential equations that embodies the compartmental model. The inverse of this matrix furnishes input resistances and voltage attenuation factors for the model, and an interactive modification of the original matrix and its inverse may be used to fit the model to anatomic and electrical measurements.

scholarly journals Application of M-Matrices for the Study of Mathematical Models of Living Systems

2018 ◽  
Vol 13 (1) ◽  
pp. 208-237 ◽  
Author(s):  
N.V. Pertsev ◽  
B.Yu. Pichugin ◽  
A.N. Pichugina
Keyword(s):  
Differential Equations ◽  
Stability Problem ◽  
Distributed Delay ◽  
Linearization Method ◽  
Living Systems ◽  
High Dimensional ◽  
Linear Differential ◽  
The Stability ◽  
Several Delays ◽  
The Right

Some results are presented of application of M-matrices to the study the stability problem of the equilibriums of differential equations used in models of living systems. The models studied are described by differential equations with several delays, including distributed delay, and by high-dimensional systems of differential equations. To study the stability of the equilibriums the linearization method is used. Emerging systems of linear differential equations have a specific structure of the right-hand parts, which allows to effectively use the properties of M-matrices. As examples, the results of studies of models arising in immunology, epidemiology and ecology are presented.

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