Hyers-Ulam Stability for Mackey-Glass and Lasota Differential Equations

Qarawani, Maher Nazmi

doi:10.5539/jmr.v5n1p34

Cited by 4 publications

(9 citation statements)

References 11 publications

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“…and so on.) On account of Lemma 1 with k = |a|, the mapping F : V → Y is the unique mapping satisfying the equalities in (13) and the inequality (14), since the inequality…”

Section: Resultsmentioning

confidence: 99%

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A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

Lee

Jung

2018

Mathematics

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“…and so on.) On account of Lemma 1 with k = |a|, the mapping F : V → Y is the unique mapping satisfying the equalities in (13) and the inequality (14), since the inequality…”

Section: Resultsmentioning

confidence: 99%

“…Since Hyers' paper, a number of mathematicians have extensively investigated the stability problems for several functional equations (see for example [2][3][4][5][7][8][9][10][11][12][13][14][15] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

Lee

Jung

2018

Mathematics

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“…Stability, for the Mackey-Glass and Lasota equations, in the sense of Hyers and Ulam has been recently reported [28].…”

Section: Introductionmentioning

confidence: 94%

Stability and Hopf bifurcation analysis of the Mackey-Glass and Lasota equations

Manjunath

Raina

2014

The 26th Chinese Control and Decision Conference (2014 CCDC)

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Mathematical models for physiological processes aid qualitative understanding of the impact of various parameters on the underlying process. We analyse two such models for human physiological processes: the Mackey-Glass and the Lasota equations, which model the change in the concentration of blood cells in the human body. We first study the local stability of these models, and derive bounds on various model parameters and the feedback delay for the concentration to equilibrate. We then deduce conditions for non-oscillatory convergence of the solutions, which could ensure that the blood cell concentration does not oscillate. Further, we define the convergence characteristics of the solutions which govern the rate at which the concentration equilibrates when the system is stable. Owing to the possibility that physiological parameters can seldom be estimated precisely, we also derive bounds for robust stability-which enable one to ensure that the blood cell concentration equilibrates despite parametric uncertainty. We also highlight that when the necessary and sufficient condition for local stability is violated, the system transits into instability via a Hopf bifurcation, leading to limit cycles in the blood cell concentration. We then outline a framework to characterise the type of the Hopf bifurcation and determine the asymptotic orbital stability of limit cycles. The analysis is complemented with numerical examples, stability charts and bifurcation diagrams. The insights into the dynamical properties of the mathematical models may serve to guide the study of dynamical diseases.

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“…There is a strong relation between fixed point theory and Ulam stability; see, e.g., [36][37][38][39][40][41]. is called generalized Ulam stable if for each ε > 0 and s ∈ M, there exists n(s) ∈ {1, 2, ...} such that for any v ∈ M satisfying the inequality:…”

Section: Ulam Stabilitymentioning

confidence: 99%

Fixed Point Results on Δ-Symmetric Quasi-Metric Space via Simulation Function with an Application to Ulam Stability

2018

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In this paper, in the setting of Δ -symmetric quasi-metric spaces, the existence and uniqueness of a fixed point of certain operators are scrutinized carefully by using simulation functions. The most interesting side of such operators is that they do not form a contraction. As an application, in the same framework, the Ulam stability of such operators is investigated. We also propose some examples to illustrate our results.

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Hyers-Ulam Stability for Mackey-Glass and Lasota Differential Equations

Abstract: This paper considers the stability of differential equation of Mackey-Glass type in the sense of Hyers and Ulam with initial condition. It also considers the Hyers-Ulam stability of Lasota equation with initial condition. Some illustrative examples are given.

Cited by 4 publications

References 11 publications

A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

Stability and Hopf bifurcation analysis of the Mackey-Glass and Lasota equations

Fixed Point Results on Δ-Symmetric Quasi-Metric Space via Simulation Function with an Application to Ulam Stability

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