0000000000282108

AUTHOR

Michael A. Radin

0000-0001-9951-7955

showing 2 related works from this author

Eventually periodic solutions of single neuron model

2020

In this paper, we consider a nonautonomous piecewise linear difference equation that describes a discrete version of a single neuron model with a periodic (period two and period three) internal decay rate. We investigated the periodic behavior of solutions relative to the periodic internal decay rate in our previous papers. Our goal is to prove that this model contains a large quantity of initial conditions that generate eventually periodic solutions. We will show that only periodic solutions and eventually periodic solutions exist in several cases.

Period (periodic table)Differential equationApplied Mathematics010102 general mathematicsMathematical analysisperiodic solutionlcsh:QA299.6-433difference equationBiological neuron modellcsh:Analysis01 natural sciencesneuron model010101 applied mathematicsPiecewise linear functioneventually periodic solution0101 mathematicsAnalysisMathematicsNonlinear Analysis: Modelling and Control
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Periodic orbits of a neuron model with periodic internal decay rate

2015

In this paper we will study a non-autonomous piecewise linear difference equation which describes a discrete version of a single neuron model with a periodic internal decay rate. We will investigate the periodic behavior of solutions relative to the periodic internal decay rate. Furthermore, we will show that only periodic orbits of even periods can exist and show their stability character.

Piecewise linear functionComputational MathematicsCharacter (mathematics)Classical mechanicsDifferential equationApplied MathematicsMathematical analysisPeriodic orbitsPeriodic sequenceBiological neuron modelStability (probability)MathematicsApplied Mathematics and Computation
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