An Introduction to Structured Population Dynamics by J. M. Cushing

By J. M. Cushing

Curiosity within the temporal fluctuations of organic populations could be traced to the sunrise of civilization. How can arithmetic be used to achieve an knowing of inhabitants dynamics? This monograph introduces the idea of based inhabitants dynamics and its purposes, concentrating on the asymptotic dynamics of deterministic types. This concept bridges the distance among the features of person organisms in a inhabitants and the dynamics of the whole inhabitants as an entire.

In this monograph, many functions that illustrate either the idea and a wide selection of organic concerns are given, besides an interdisciplinary case examine that illustrates the relationship of types with the information and the experimental documentation of version predictions. the writer additionally discusses using discrete and non-stop types and provides a normal modeling thought for dependent inhabitants dynamics.

Cushing starts off with an noticeable element: members in organic populations fluctuate with reference to their actual and behavioral features and consequently within the manner they have interaction with their setting. learning this element successfully calls for using established versions. particular examples brought up all through help the precious use of dependent versions. integrated between those are vital purposes selected to demonstrate either the mathematical theories and organic difficulties that experience obtained cognizance in fresh literature.

Show description

Read Online or Download An Introduction to Structured Population Dynamics PDF

Similar probability books

Probability and Theory of Errors (Fourth Edition)

This can be a pre-1923 old copy that was once curated for caliber. caliber insurance was once carried out on every one of those books in an try and eliminate books with imperfections brought through the digitization approach. even though we have now made top efforts - the books could have occasional error that don't hamper the analyzing adventure.

Quantum Probability and Related Topics: Proceedings of the 30th Conference

This quantity comprises present paintings on the frontiers of analysis in quantum chance, limitless dimensional stochastic research, quantum details and facts. It provides a gently selected selection of articles by way of specialists to focus on the newest d

Additional info for An Introduction to Structured Population Dynamics

Example text

42) that v'(p) < 0 for all p > 0 and limp_,+00 v(p) = 0. 5 we find that x = 0 loses stability as n increases through 1. 2) and there exists a unique positive equilibrium these positive equilibria are (locally asymptotically) stable for n w 1 and are unbounded as n —> +00. , limt_+00 \x(t)\ = 0 for all x(0) > 0). In the preceding example only the facts that the submodels for the fertilities and transition probabilities tend monotonically to 0 as p increases without bound were used. Thus, other nonlinearities (or a mix of nonlinearities).

It is shown in [112] that only one of the two bifurcating branches can be stable. Specifically, the positive equilibrium branch is stable near n = 1 if 1. See Fig. 11. For large values of n the situation is more complicated, however; see [112]. 4 A case study Can mathematical models be used to describe and predict the dynamics of a real biological population? Can model predicted dynamics be observed in population data? Can predicted bifurcations in dynamics be observed in a population when DISCRETE MODELS 47 physical or biological parameters are changed?

D against the parameter b. In (a). 5. 20. To eliminate transients, 1000 iterations were performed before 100 values of p were plotted. in B,\ x R^_ and is (locally asymptotically) stable near the bifurcation point. The inequalities above (which are valid for all solutions, including equilibrium solutions) show that the magnitude of equilibria are bounded above by a multiple of n, and from this it follows that the spectrum of the continuum cannot be bounded (for if it were, then the global continuum would be bounded).

Download PDF sample

Rated 4.79 of 5 – based on 10 votes