Existence and Qualitative Properties of Solutions of a Second Order Mixed Type Impulsive Differential Equation with Piecewise Constant Arguments

Oztepe, Gizem S.

doi:10.15672/hjms.2017.431

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References 23 publications

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“…Of course, the qualitative study for nonlinear impulsive difference equations of type (E) may be helpful for lossless transmission lines models in high speed computers. For our study, we refer to the monograph [4] by Lakshmikantham et al and some related works [3], [5], [6], [7], [13], [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Second Order Impulsive Difference Equations and their Oscillation Properties

Tripathy

Chhatria

2020

Tatra Mountains Mathematical Publications

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Section: Introductionmentioning

confidence: 99%

Nonlinear Second Order Impulsive Difference Equations and their Oscillation Properties

Tripathy

Chhatria

2020

Tatra Mountains Mathematical Publications

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Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments

Kartal

2023

Cumhuriyet Science Journal

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In this study, we analyze a cancer model which includes the interactions among tumor cells, healthy host cells and effector immune cells. The model with continuous case has been studied in the literature and it has been shown that it exhibits chaotic behavior. In this paper, we aim to build a better understanding of how both discrete and continuous times affect the dynamic behavior of the tumor growth model. So, we reconsider the model as a system of differential equations with piecewise constant argument. To analyze dynamical behavior of the model, we consider the solution of the system in a certain subinterval which leads to the system of difference equations. Some theoretical results are obtained for local behavior of the system. In addition, we study chaotic dynamic of the system through Neimark-Sacker bifurcation by using Lyapunov exponents

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Existence and Qualitative Properties of Solutions of a Second Order Mixed Type Impulsive Differential Equation with Piecewise Constant Arguments

Abstract: We prove the existence and uniqueness of the solutions of a second order mixed type impulsive differential equation with piecewise constant arguments. Moreover, we study oscillation, non-oscillation and periodicity of the solutions.

Cited by 2 publications

References 23 publications

Nonlinear Second Order Impulsive Difference Equations and their Oscillation Properties

Nonlinear Second Order Impulsive Difference Equations and their Oscillation Properties

Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments

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