Deterministic Mathematical Models in Population Ecology.
About: This article is published in American Mathematical Monthly.The article was published on 1982-12-01. It has received 19 citations till now. The article focuses on the topics: Quantitative ecology & Population ecology.
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TL;DR: In this article, the authors suggest empirical multivariate studies of landscape change, modelling of individual landscape processes, explicit study of the effect of model scale on model behavior, and scaling-up results of studies, on smaller land areas, that have landscape relevance.
Abstract: Models of landscape change may serve a variety of purposes, from exploring the interaction of natural processes to evaluating proposed management treatments These models can be categorized as either whole landscape models, distributional landscape models, or spatial landscape models, depending on the amount of detail included in the models Distributional models, while widely used, exclude spatial detail important for most landscape ecological research Spatial models require substantial data, now more readily available, via remote sensing, and more easily manipulated, in geographical information systems In spite of these technical advances, spatial modelling is poorly developed, largely because landscape change itself is poorly understood To facilitate further development of landscape models I suggest (1) empirical multivariate studies of landscape change, (2) modelling of individual landscape processes, (3) explicit study of the effect of model scale on model behavior, and (4) ‘scaling-up’ results of studies, on smaller land areas, that have landscape relevance
510 citations
Cites methods from "Deterministic Mathematical Models i..."
...Comparable models have been applied in a variety of other fields (e.g., Freedman 1980; Nisbet and Gurney 1982; Edelstein-Keshet 1988) too, numerous to review here....
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TL;DR: In this paper, a discrete predator-prey system with delay is considered and a sufficient condition for the uniform persistence of the system is given, assuming that the coefficients in the system are periodic, by generalizing the Yoshizawa's theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays.
97 citations
Cites background from "Deterministic Mathematical Models i..."
...On the other hand, ma thors [1,2,4,10] have argued that the discrete time models governed by difference eq are more appropriate than the continuous ones when the populations have nono ping generations....
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TL;DR: In this article, the authors studied the trajectory behavior of Lotka-Volterra competition bistable systems and systems with telegraph noises and proved that there exists a unique solution, bounded above and below by positive constants.
93 citations
42 citations
TL;DR: By using the continuation theorem of coincidence degree theory, sufficient criteria were obtained for the existence of periodic solutions of the mutualism model in this paper, and sufficient conditions were obtained by using Mawhin's continuation theorem.
33 citations
Cites background from "Deterministic Mathematical Models i..."
...Since many authors [1,2,7,13] have argued that the discrete time models governed by difference equations are more appropriate than the continuous ones when the populations have non-overlapping generations, also, since discrete time models can also provide efficient computational models of continuous models for numerical simulations, it is reasonable to study discrete time food-chain models governed by difference equations....
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References
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TL;DR: In this article, the authors suggest empirical multivariate studies of landscape change, modelling of individual landscape processes, explicit study of the effect of model scale on model behavior, and scaling-up results of studies, on smaller land areas, that have landscape relevance.
Abstract: Models of landscape change may serve a variety of purposes, from exploring the interaction of natural processes to evaluating proposed management treatments These models can be categorized as either whole landscape models, distributional landscape models, or spatial landscape models, depending on the amount of detail included in the models Distributional models, while widely used, exclude spatial detail important for most landscape ecological research Spatial models require substantial data, now more readily available, via remote sensing, and more easily manipulated, in geographical information systems In spite of these technical advances, spatial modelling is poorly developed, largely because landscape change itself is poorly understood To facilitate further development of landscape models I suggest (1) empirical multivariate studies of landscape change, (2) modelling of individual landscape processes, (3) explicit study of the effect of model scale on model behavior, and (4) ‘scaling-up’ results of studies, on smaller land areas, that have landscape relevance
510 citations
TL;DR: In this paper, non-constant positive steady-state solutions of a predator-prey system with non-monotonic functional response, also called Holling type-IV interaction terms, and diffusion under the homogeneous Neumann boundary condition are investigated.
Abstract: This paper deals with non-constant positive steady-state solutions of a predator-prey system with non-monotonic functional response, also called Holling type-IV interaction terms, and diffusion under the homogeneous Neumann boundary condition. We first establish positive upper and lower bounds for such solutions, and then study their non-existence, global existence and bifurcation.
115 citations
TL;DR: In this paper, a discrete predator-prey system with delay is considered and a sufficient condition for the uniform persistence of the system is given, assuming that the coefficients in the system are periodic, by generalizing the Yoshizawa's theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays.
97 citations
TL;DR: In this article, the authors studied the trajectory behavior of Lotka-Volterra competition bistable systems and systems with telegraph noises and proved that there exists a unique solution, bounded above and below by positive constants.
93 citations
TL;DR: By using the continuation theorem of coincidence degree theory, sufficient criteria were obtained for the existence of periodic solutions of the mutualism model in this paper, and sufficient conditions were obtained by using Mawhin's continuation theorem.
33 citations