An Introduction to Difference Equations

Elaydi, Saber

doi:10.1007/978-1-4757-9168-6

Cited by 565 publications

(511 citation statements)

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“…We note that Schur stability of a polynomial can be determined by checking some inequalities in terms of its coefficients; this is known as the Jury test, see [23]. We will apply this test to (6) later.…”

Section: Remarkmentioning

confidence: 99%

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On the stability of delayed feedback controllers

Morgül

2003

Physics Letters A

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We consider the stability of delayed feedback control (DFC) scheme for one-dimensional discrete time systems. We first construct a map whose fixed points correspond to the periodic orbits of the uncontrolled system. Then the stability of the DFC is analyzed as the stability of the corresponding equilibrium point of the constructed map. For each periodic orbit, we construct a characteristic polynomial whose Schur stability corresponds to the stability of DFC. By using Schur-Cohn criterion, we can find bounds on the gain of DFC to ensure stability.

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Section: Remarkmentioning

confidence: 99%

“…We note that the Schur stability of a polynomial can be checked by applying the so-called Schur-Cohn criterion, or equivalently the Jury test to the polynomial, see [23]. This test gives some necessary and sufficient conditions on the coefficients of the polynomial.…”

Section: Remarkmentioning

confidence: 99%

On the stability of delayed feedback controllers

Morgül

2003

Physics Letters A

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“…, I a , I v ) ∈ : I a = I v = 0} and the only invariant set in M is ( a /µ a , 0, 0). Therefore, ( a /µ a , 0, 0) is globally asymptotically stable for system (3.9) by the LaSalle's invariance principle [8,14]. Since the limiting system (3.9) has only one equilibrium which is moreover globally asymptotically stable when R 0 ≤ 1, applying [6], we conclude that the disease-free equilibrium is globally asymptotically stable for system (2.2) when α a = 0, 0 ≤ p < 1, and R 0 ≤ 1.…”

Section: Theorem 34 the Disease-free Equilibriummentioning

confidence: 95%

On a discrete West Nile epidemic model

Jang¹

2007

Mat. apl. comput.

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“…In this section, however, the values of r and K that give rise to a stable equilibrium τ > 0 with F (τ ) = τ = K is chosen for the purpose of illustration. More general discussions with respect to dynamic behaviors of difference equations can be found in May (1974) and Elaydi (2005).…”

Section: Numerical Analysismentioning

confidence: 99%

Dynamic economic analysis on invasive species management: Some policy implications of catchability

Kotani

Kakinaka

Matsuda

2009

Mathematical Biosciences

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The problems of controlling invasive species have been emerging as a global issue. In response to these threats, some governmental programs have been proposed for supporting eradication. This article challenges this view by studying the optimal strategies of controlling invasive species in a simple dynamic model. The analysis mainly focuses on deriving policy implications of catchability in a situation where a series of controlling actions incurs operational costs that derive from the fact that catchability depends on the current stock size of invasive species. We analytically demonstrate that the optimal policy sequence can drastically change, depending on the sensitivity of catchability in response to a change in the stock size, as well as on the initial stock. If the sensitivity of catchability is sufficiently high, the constant escapement policy with some interior target level is optimal. In contrast, if the sensitivity of catchability is sufficiently low, there could exist a threshold of the initial stock which differentiates the optimal policy between immediate eradication and giving-up without any control. In the intermediate range, immediate eradication, giving-up without any control, or more complex policies might be optimal. Numerical analysis is employed to present economic intuitions and insights in both analytically tractable and intractable cases.

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An Introduction to Difference Equations

Cited by 565 publications

References 0 publications

On the stability of delayed feedback controllers

On the stability of delayed feedback controllers

On a discrete West Nile epidemic model

Dynamic economic analysis on invasive species management: Some policy implications of catchability

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