Neuron model with a period three internal decay rate

Inese Bula; Michael A. Radin; Nicholas Wilkins

doi:10.14232/ejqtde.2017.1.46

Neuron model with a period three internal decay rate

Inese Bula^*
, Michael A. Radin
, Nicholas Wilkins

^*Corresponding author for this work

Department of Mathematics

University of Latvia
Rochester Institute of Technology

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper we will study a non-autonomous piecewise linear difference equation that describes a discrete version of a single neuron model. We will investigate the periodic behavior of solutions relative to the sequence periodic with period three internal decay rate. In fact, we will show that only periodic cycles with period 3k, k=1,2,3,… can exist and also show their stability character.

Original language	English
Pages (from-to)	1-19
Number of pages	19
Journal	Electronic Journal of Qualitative Theory of Differential Equations
Volume	2017
DOIs	https://doi.org/10.14232/ejqtde.2017.1.46
Publication status	Published - 2017

Keywords

Difference equation
Neuron model
Periodic orbits
Stability

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10.14232/ejqtde.2017.1.46

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title = "Neuron model with a period three internal decay rate",

abstract = "In this paper we will study a non-autonomous piecewise linear difference equation that describes a discrete version of a single neuron model. We will investigate the periodic behavior of solutions relative to the sequence periodic with period three internal decay rate. In fact, we will show that only periodic cycles with period 3k, k=1,2,3,… can exist and also show their stability character.",

keywords = "Difference equation, Neuron model, Periodic orbits, Stability",

author = "Inese Bula and Radin, \{Michael A.\} and Nicholas Wilkins",

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language = "English",

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T1 - Neuron model with a period three internal decay rate

AU - Bula, Inese

AU - Radin, Michael A.

AU - Wilkins, Nicholas

PY - 2017

Y1 - 2017

N2 - In this paper we will study a non-autonomous piecewise linear difference equation that describes a discrete version of a single neuron model. We will investigate the periodic behavior of solutions relative to the sequence periodic with period three internal decay rate. In fact, we will show that only periodic cycles with period 3k, k=1,2,3,… can exist and also show their stability character.

AB - In this paper we will study a non-autonomous piecewise linear difference equation that describes a discrete version of a single neuron model. We will investigate the periodic behavior of solutions relative to the sequence periodic with period three internal decay rate. In fact, we will show that only periodic cycles with period 3k, k=1,2,3,… can exist and also show their stability character.

KW - Difference equation

KW - Neuron model

KW - Periodic orbits

KW - Stability

UR - https://www.scopus.com/pages/publications/85021269808

U2 - 10.14232/ejqtde.2017.1.46

DO - 10.14232/ejqtde.2017.1.46

M3 - Article

AN - SCOPUS:85021269808

SN - 1417-3875

VL - 2017

SP - 1

EP - 19

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

ER -

Neuron model with a period three internal decay rate

Abstract

Keywords

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