Piecewise linear differential equations and integrate-and-fire neurons: Insights from two-dimensional membrane models

Physical Review E ◽

10.1103/physreve.67.021908 ◽

2003 ◽

Vol 67 (2) ◽

Author(s):

Arnaud Tonnelier ◽

Wulfram Gerstner

Keyword(s):

Differential Equations ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Two Dimensional ◽

Integrate And Fire ◽

Membrane Models ◽

Linear Differential

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Frequency Coupling Matrix of a Voltage-Source Converter Derived From Piecewise Linear Differential Equations

IEEE Transactions on Power Delivery ◽

10.1109/tpwrd.2006.886779 ◽

2007 ◽

Vol 22 (3) ◽

pp. 1603-1612 ◽

Author(s):

P. W. Lehn ◽

K. L. Lian

Keyword(s):

Differential Equations ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Voltage Source ◽

Voltage Source Converter ◽

Coupling Matrix ◽

Frequency Coupling ◽

Linear Differential

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Planar systems of piecewise linear differential equations with a line of discontinuity

Nonlinearity ◽

10.1088/0951-7715/14/6/311 ◽

2001 ◽

Vol 14 (6) ◽

pp. 1611-1632 ◽

Author(s):

Fotios Giannakopoulos ◽

Karin Pliete

Keyword(s):

Differential Equations ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Line Of Discontinuity ◽

Planar Systems ◽

Linear Differential

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Periodic solutions in systems of piecewise- linear differential equations

Dynamics and Stability of Systems ◽

10.1080/02681119508806202 ◽

1995 ◽

Vol 10 (2) ◽

pp. 179-193 ◽

Author(s):

Thomas Mestl ◽

Erik Plahte ◽

Stig W. Omholt

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Linear Differential

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Efficient solution of the variational equation for piecewise-linear differential equations

International Journal of Circuit Theory and Applications ◽

10.1002/cta.4490140404 ◽

1986 ◽

Vol 14 (4) ◽

pp. 305-314 ◽

Author(s):

Thomas S. Parker ◽

Leon O. Chua

Keyword(s):

Differential Equations ◽

Efficient Solution ◽

Variational Equation ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Linear Differential

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Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach

Dynamics and Stability of Systems ◽

10.1080/02681118908806072 ◽

1989 ◽

Vol 4 (3-4) ◽

pp. 565-583 ◽

Author(s):

El Houssine Snoussi

Keyword(s):

Differential Equations ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Mapping Approach ◽

Qualitative Dynamics ◽

Linear Differential

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A class of piecewise linear differential equations arising in biological models

Dynamical Systems ◽

10.1080/1468936021000041681 ◽

2002 ◽

Vol 17 (4) ◽

pp. 299-316 ◽

Author(s):

Jean-Luc Gouzé ◽

Tewfik Sari

Keyword(s):

Differential Equations ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Biological Models ◽

Linear Differential

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Piecewise-linear approximation of solution of linear differential equations by Walsh functions

Mathematics and Computers in Simulation ◽

10.1016/0378-4754(90)90186-m ◽

1990 ◽

Vol 32 (3) ◽

pp. 297-308

Author(s):

Masaaki Ohkita ◽

Yasuhiro Kobayashi

Keyword(s):

Differential Equations ◽

Linear Approximation ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Piecewise Linear Approximation ◽

Walsh Functions ◽

Linear Differential

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Comments on ‘efficient solution of the variational equation for piecewise-linear differential equations’

International Journal of Circuit Theory and Applications ◽

10.1002/cta.4490160305 ◽

1988 ◽

Vol 16 (3) ◽

pp. 325-329 ◽

Author(s):

Thomas S. Parker ◽

Leon O. Chua ◽

Martin Hasler

Keyword(s):

Differential Equations ◽

Efficient Solution ◽

Variational Equation ◽

Piecewise Linear ◽

Linear Differential Equations ◽

Linear Differential

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Asymptotic stability of two dimensional systems of linear difference equations and of second order half-linear differential equations with step function coefficients

Electronic journal of qualitative theory of differential equations ◽

10.14232/ejqtde.2011.1.38 ◽

2011 ◽

pp. 1-17 ◽

Author(s):

L. Székely ◽

László Hatvani

Keyword(s):

Asymptotic Stability ◽

Differential Equations ◽

Difference Equations ◽

Step Function ◽

Second Order ◽

Linear Differential Equations ◽

Two Dimensional ◽

Linear Difference Equations ◽

Linear Differential

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Numerical Solution of a Two-Point Boundary-Value Problem for a System of Linear Differential Equations with Nonlinear Two-Dimensional Spectral Parameter

Journal of Mathematical Sciences ◽

10.1007/s10958-020-04790-5 ◽

2020 ◽

Vol 247 (1) ◽

pp. 73-87

Author(s):

P. О. Savenko

Keyword(s):

Differential Equations ◽

Boundary Value Problem ◽

Numerical Solution ◽

Spectral Parameter ◽

Boundary Value ◽

Linear Differential Equations ◽

Two Dimensional ◽

Point Boundary ◽

Linear Differential

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