2010
DOI: 10.1007/978-3-642-14258-1
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Geometric Theory of Discrete Nonautonomous Dynamical Systems

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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Cited by 109 publications
(95 citation statements)
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“…See [9] for a discussion of some new examples of models exhibiting the Allee effect and, similar to the Beverton-Holt model, having important biological quantities as parameters, for example, intrinsic growth rate, carrying capacity, Allee threshold, and a new parameter, the shock recovery parameter. Further references pertaining to the Allee effect can be found in [1,3,4,6,[10][11][12][16][17][18]23,26,31,32], and for references to the general theory of difference equations, see [7,20]. For a discussion on the use of the Sigmoid model, see [28, p. 82] In what follows, we show that under certain conditions on the coefficients, Equation (1) has an asymptotically stable p-periodic state and an unstable p-periodic Allee state.…”
Section: Introductionmentioning
confidence: 75%
“…See [9] for a discussion of some new examples of models exhibiting the Allee effect and, similar to the Beverton-Holt model, having important biological quantities as parameters, for example, intrinsic growth rate, carrying capacity, Allee threshold, and a new parameter, the shock recovery parameter. Further references pertaining to the Allee effect can be found in [1,3,4,6,[10][11][12][16][17][18]23,26,31,32], and for references to the general theory of difference equations, see [7,20]. For a discussion on the use of the Sigmoid model, see [28, p. 82] In what follows, we show that under certain conditions on the coefficients, Equation (1) has an asymptotically stable p-periodic state and an unstable p-periodic Allee state.…”
Section: Introductionmentioning
confidence: 75%
“…In this section we reexamine our problem from that point of view. We refer the reader to [7,23,[25][26][27], [20,Sections 3.2 and 3.3], and references therein for a detailed account of this theory. For the reader's convenience, we state the results that we will need in the paper.…”
Section: A Bifurcation Analysismentioning
confidence: 99%
“…(iv) A different definition of a Bohl spectrum for discrete systems depending on certain invariant splittings was proposed in [25,Definition 3.8.1], and another spectrum between the Lyapunov and Sacker-Sell spectrum based on nonuniform exponential dichotomies was introduced in [12].…”
Section: The Bohl Spectrummentioning
confidence: 99%