Dynamical properties of some rational systems of difference equations

Khan, A. Q.; Qureshi, S. M.

doi:10.1002/mma.6955

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…A single normal cycle of the ECG represents the successive atrial depolarization/repolarization and ventricular depolarization/repolarization which occurs with every heartbeat. These can be approximately associated with the peaks and troughs of the ECG waveform labeled P, Q, R, S, and T as shown in figure 9 Figure 9: Morphology of a mean PQRST-complex of an ECG recorded from a normal human Extracting useful clinical information from the real (noisy) ECG requires reliable signal processing techniques [AL Goldberger,E Goldberger (1977)]. These include R-peak detection [Jiapu Pan; Willis J.…”

Section: Phase Plane Diagramsmentioning

confidence: 99%

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On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0< a ≤ 2 and its application in medicine

Rafik

humberto

Martínez

2022

Preprint

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Recently, mathematicians have been interested in studying the theory of discrete dynamical system, specifically difference equation, such that considerable works about discussing the behavior properties of its solutions (boundedness and unboundedness) are discussed and published in many areas of mathematics which involves several interesting results and applications in applied mathematics and physics, One of the most important discrete dynamics which is become of interest for researchers in the field is the rational dynamical system. In this paper we may discuss qualitative behavior and properties of the difference equation xn+1=ax2n+bx2n-1 with a and b are two parameters and we shall show its application to medicine

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Section: Phase Plane Diagramsmentioning

confidence: 99%

“…The study of nonlinear rational difference equations of higher order is of paramount importance, since we still know so little about such equations. In this paper [A. Q. Khan,S. M. Qureshi (2020)] A. Q.…”

Section: Introductionmentioning

confidence: 99%

On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0< a ≤ 2 and its application in medicine

Rafik

humberto

Martínez

2022

Preprint

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“…Difference equations (systems) play a crucial role in the development of a variety of disciplines (see, e.g., previous studies 1‐38 and references cited therein). The exponential form is one of the most diverse types of difference equations.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of a difference equation model in exponential form

Ibrahim

2022

Math Methods in App Sciences

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We investigate the global stability and the convergence rate of the exponential model:and u −2 and the parameters 𝜇 1 , 𝜆 1 , 𝜆 2 , 𝜇 3 , 𝜆 3 , 𝜇 2 , 𝜆 4 , and 𝜇 4 are non-negative real numbers. We also discuss the unboundedness, persistence, and boundedness of this system. Moreover, we introduce conditions for uniqueness and existence of the equilibrium. Finally, we give numerical explanations to verify our results. We can use the above system as a model for the growth of some perennial plants and their relationships with each other. KEYWORDS asymptotic global and local stability, boundedness, persistence, the rate of convergence, unboundedness MSC CLASSIFICATION 40A05, 39A10 INTRODUCTIONDifference equations (systems) play a crucial role in the development of a variety of disciplines (see, e.g., previous studies and references cited therein). The exponential form is one of the most diverse types of difference equations. Such structures have many topics in our life. For example, El-Metwally et al 8 worked out the difference equation for a population model: Ma et al. 33 examined the equation:where b, a ≥ 0 and the initials are positive numbers. Feng et al. 12 studied a model for the production of a biennial plant in the following form:where c 1 , c 3 ∈ (0, ∞) and c 2 ∈ (0, 1).

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Dynamics and Solutions’ Expressions of a Higher-Order Nonlinear Fractional Recursive Sequence

Alshareef

Alzahrani

Khan

2021

Mathematical Problems in Engineering

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The principle purpose of this article is to examine some stability properties for the fixed point of the below rational difference equation U n + 1 = ξ U n − 8 + ε U n − 8 2 / μ U n − 8 + κ U n − 17 where ξ , ε , μ , and κ are arbitrary real numbers. Moreover, solutions for some special cases of the proposed difference equation are introduced.

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Dynamical properties of some rational systems of difference equations

Cited by 4 publications

References 29 publications

On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0< a ≤ 2 and its application in medicine

On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0< a ≤ 2 and its application in medicine

Asymptotic behavior of a difference equation model in exponential form

Dynamics and Solutions’ Expressions of a Higher-Order Nonlinear Fractional Recursive Sequence

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Dynamical properties of some rational systems of difference equations

Cited by 4 publications

References 29 publications

On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0&lt; a ≤ 2 and its application in medicine

On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0&lt; a ≤ 2 and its application in medicine

Asymptotic behavior of a difference equation model in exponential form

Dynamics and Solutions’ Expressions of a Higher-Order Nonlinear Fractional Recursive Sequence

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On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0< a ≤ 2 and its application in medicine

On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0< a ≤ 2 and its application in medicine