Global dynamics in a stage-structured discrete-time population model with harvesting

Liz, Eduardo; Pilarczyk, Paweł

doi:10.1016/j.jtbi.2011.12.012

Cited by 50 publications

(38 citation statements)

References 42 publications

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“…Finally, these maps are robust with respect to either numerical or experimental perturbation. This strongly suggests that this approach provides a framework in which to develop a new computational theory of nonlinear dynamics, and the first steps in this direction have been taken [2,5,4,12]. For any given dynamical system ϕ, Att(ϕ) has at most countable elements while ANbhd(ϕ) typically contains uncountably many elements.…”

Section: Throughout This Paper We Make the Following Assumptionmentioning

confidence: 99%

Lattice structures for attractors I

Kalies¹,

Mischaikow²,

Vandervorst³

2014

Journal of Computational Dynamics

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ABSTRACT. We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and noninvertible. We separate those properties which rely solely on algebraic structures from those that require some topological arguments, in order to lay a foundation for the development of algorithms to manipulate these structures computationally.

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Section: Throughout This Paper We Make the Following Assumptionmentioning

confidence: 99%

Lattice structures for attractors I

Kalies¹,

Mischaikow²,

Vandervorst³

2014

Journal of Computational Dynamics

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“…Another system of type (2a) and (2b) is the autonomous stage-structured model with harvesting that is discussed in [10,11], which may be written as…”

Section: Introductionmentioning

confidence: 99%

“…Compensatory recruitment is used in populations where recruitment increases with increase in densities before reaching an asymptote, while in overcompensatory models recruitment declines as density increases (see [11,14]). A thorough analysis of the dynamics of (4a) and (4b) with the Ricker function appears in [10]. The results in [10,11] clarify many issues with regard to the effects of harvesting in stage-structured models such as global convergence to 0 and the existence of a stable survival equilibrium as well as the so-called hydra effect for different harvesting scenarios and with different recruitment functions; this refers to the counter-intuitive situation where an increase in the harvest or mortality rate results in a corresponding increase in the total population; for example, see [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of Planar Systems That Model Stage-Structured Populations

Lazaryan

Sedaghat

2015

Discrete Dynamics in Nature and Society

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We study a general discrete planar system for modeling stage-structured populations. Our results include conditions for the global convergence of orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are periodic we obtain weaker conditions for extinction. We also study a rational special case of the system for Beverton-Holt type interactions and show that the persistence equilibrium (in the positive quadrant) may be globally attracting even in the presence of interstage competition. However, we determine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and the system exhibits period two oscillations.

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“…in a method for editing vector fields and extraction of periodic orbits [8], and also very helpful in an automatic method for classification of dynamics in multi-parameter systems [4,7], which found applications e.g. in population biology [38] and in physics of plasmas [49]. Homology has also been proposed as a reliable criterion for thinning binary images of arbitrary dimension [46].…”

Section: Introductionmentioning

confidence: 99%

Computation of cubical homology, cohomology, and (co)homological operations via chain contraction

Pilarczyk

Real

2014

Adv Comput Math

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We introduce algorithms for the computation of homology, cohomology, and related operations on cubical cell complexes, using the technique based on a chain contraction from the original chain complex to a reduced one that represents its homology. This work is based on previous results for simplicial complexes, and uses Serre's diagonalization for cubical cells. An implementation in C++ of the intro-duced algorithms is available at http://www.pawelpilarczyk.com/chaincon/ together with some examples. The paper is self-contained as much as possible, and is written at a very elementary level, so that basic knowledge of algebraic topology should be sufficient to follow it.

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Global dynamics in a stage-structured discrete-time population model with harvesting

Cited by 50 publications

References 42 publications

Lattice structures for attractors I

Lattice structures for attractors I

Dynamics of Planar Systems That Model Stage-Structured Populations

Computation of cubical homology, cohomology, and (co)homological operations via chain contraction

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