On the periodic logistic equation

AlSharawi, Ziyad; Angelos, James

doi:10.1016/j.amc.2005.12.016

Cited by 19 publications

(15 citation statements)

References 14 publications

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“…The main contribution in this area are the papers by Henson [11], AlSharawi and Angelo [3], and Oliveira and D'Aniello [14]. Our main goal here is to give precise and complete definitions and notions for the various bifurcation notions in the setting of nonautonomous systems.…”

Section: Bifurcationmentioning

confidence: 99%

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Non-autonomous periodic systems with Allee effects

Luís

Elaydi

Oliveira

2010

Journal of Difference Equations and Applications

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A new class of maps called unimodal Allee maps are introduced. Such maps arise in the study of population dynamics in which the population goes extinct if its size falls below a threshold value. A unimodal Allee map is thus a unimodal map with tree fixed points, a zero fixed point, a small positive fixed point, called threshold point, and a bigger positive fixed point, called the carrying capacity. In this paper the properties and stability of the three fixed points are studied in the setting of nonautonomous periodic dynamical systems or difference equations. Finally we investigate the bifurcation of periodic systems/difference equations when the system consists of two unimodal Allee maps.

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Section: Bifurcationmentioning

confidence: 99%

“…Stability notions for periodic difference equations have been investigated by many authors. Including, to cite few, AlSharawi and Angelos [3], AlSharawi, Angelos, Elaydi and Rakesh [4], Henson [11], Yakubu [15], Oliveira and D'Aniello [14], and Selgrado and Roberds [20].…”

Section: Stabilitymentioning

confidence: 99%

Non-autonomous periodic systems with Allee effects

Luís

Elaydi

Oliveira

2010

Journal of Difference Equations and Applications

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“…It should be pointed out here that equation (2) or equation (3) may not generate a discrete semidynamical system as it may not satisfy the semigroup property. The following example illustrates this point.…”

Section: π(π(X S) T) = π(X S + T) S T ∈ Z and X ∈ X (The Group Pmentioning

confidence: 99%

“…The main contribution in this area are the papers by Henson [24], Al-Sharawi and Angelos [2], Oliveira and D'Aniello [30], and recently Luís, Elaydi and Oliveira [29].…”

Section: Bifurcationmentioning

confidence: 99%

“…So, for the system W, unfortunately we are unable to draw these curves for the 4−periodic cycle. However, it should be noted that AlSharawi and Angelos [2] have used the command "resultant" to investigate the bifurcations of the periodically forced logistic map, and they were able to draw these curves for the 4−periodic cycles of the 2−periodic system. Moreover, these authors drew the bifurcation surfaces for the 3−periodic cycle of the 3−periodic system in the three dimensional space of the parameters.…”

Section: For the Saddle-node Bifurcation We Then Solve The Equationsmentioning

confidence: 99%

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Towards a Theory of Periodic Difference Equations and Its Application to Population Dynamics

Elaydi

Luís

Oliveira

2011

Dynamics, Games and Science I

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This survey contains the most updated results on the dynamics of periodic difference equations or discrete dynamical systems this time. Our focus will be on stability theory, bifurcation theory, and on the effect of periodic forcing on the welfare of the population (attenuance versus resonance). Moreover, the survey alludes to two more types of dynamical systems, namely, almost periodic difference equations and stochastic difference equations.

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