Jim M. Cushing

Bio: Jim M. Cushing is an academic researcher from University of Arizona. The author has contributed to research in topics: Population & Nonlinear system. The author has an hindex of 41, co-authored 169 publications receiving 8061 citations. Previous affiliations of Jim M. Cushing include IBM & College of William & Mary.

An introduction to structured population dynamics

Abstract: Preface 1 Discrete Models Matrix Models Autonomous Single Species Models Some Applications A Case Study Multispecies Interactions 2 Continuous Models Age-Structured Models Autonomous Age-Structured Models Some Applications Multispecies Interactions Other Structured Models 3 Population Level Dynamics Ergodicity and Nonlinear Models The Linear Chain Trick Hierarchical Models Total Population Size in Age-Structured Models Appendix A Stability Theory for Maps Linear Maps Linearization of Maps Appendix B Bifurcation Theorems A Global Bifurcation Theorem Local Parameterization Appendix C Miscellaneous Proofs Bibliography Index

Integrodifferential Equations and Delay Models in Population Dynamics

Abstract: 1: Introductory Remarks.- 2: Some Preliminary Remarks on Stability.- 2.1 Linearization.- 2.2 Autonomous Linear Systems.- 3: Stability and Delay Models for a Single Species.- 3.1 Delay Logistic Equations.- 3.2 The Logistic Equation with a Constant Time Lag.- 3. 3 Some Other Models.- 3.4 Some General Results.- 3.5 A General Instability Result.- 3.6 The Stabilizing Effect of Delays.- 4: Stability and Multi-Species Interactions with Delays.- 4.1 Volterra's Predator-Prey Model with Delays.- 4. 2 Predator-Prey Models with Density Terms.- 4.3 Predator-Prey Models with Response Delays to Resource Limitation.- 4.4 Stability and Vegetation-Herbivore-Carnivore Systems.- 4.5 Some Other Delay Predator-Prey Models.- 4.6 The Stabilization of Predator-Prey Interactions.- 4.7 A General Predator-Prey Model.- 4.8 Competition and Mutualism.- 4.9 Stability and Instability of n-Species Models.- 4.10 Delays Can Stabilize an Otherwise Unstable Equilibrium.- 5: Oscillations and Single Species Models with Delays.- 5.1 Single Species Models and Large Delays.- 5.2 Bifurcation of Periodic Solutions of the Delay Logistic.- 5.3 Other Results on Nonconstant Periodic Solutions.- 5.4 Periodically Fluctuating Environments.- 6: Oscillations and Multi-Species Interactions with Delays.- 6.1 A General Bifurcation Theoren.- 6.2 Periodic Oscillations Due to Delays in Predator-Prey Interactions..- 6.3 Numerically Integrated Examples of Predator-Prey Models with Delays.- 6.4 Oscillations and Predator-Prey Models with Delays.- 6.5 Two Species Competition Models with Linear Response Functionals.- 6.6 Two Species Mutualism Models with Linear Response Functionals.- 6.7 Delays in Systems with More than Two Interacting Species.- 6.8 Periodically Fluctuating Environments.- 7: Some Miscellaneous Topics.- References.

Bifurcation Analysis of a Mathematical Model for Malaria Transmission

Abstract: We present an ordinary differential equation mathematical model for the spread of malaria in human and mosquito populations. Susceptible humans can be infected when they are bitten by an infectious mosquito. They then progress through the exposed, infectious, and recovered classes, before reentering the susceptible class. Susceptible mosquitoes can become infected when they bite infectious or recovered humans, and once infected they move through the exposed and infectious classes. Both species follow a logistic population model, with humans having immigration and disease‐induced death. We define a reproductive number, $R_0$, for the number of secondary cases that one infected individual will cause through the duration of the infectious period. We find that the disease‐free equilibrium is locally asymptotically stable when $R_0 1$. We prove the existence of at least one endemic equilibrium point for all $R_0 > 1$. In the absence of disease‐induced death, we prove that the tran...

Chaotic Dynamics in an Insect Population

Abstract: A nonlinear demographic model was used to predict the population dynamics of the flour beetle Tribolium under laboratory conditions and to establish the experimental protocol that would reveal chaotic behavior. With the adult mortality rate experimentally set high, the dynamics of animal abundance changed from equilibrium to quasiperiodic cycles to chaos as adult-stage recruitment rates were experimentally manipulated. These transitions in dynamics corresponded to those predicted by the mathematical model. Phase-space graphs of the data together with the deterministic model attractors provide convincing evidence of transitions to chaos.

Human biochemical genetics

Abstract: So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

The ontogenetic niche and species interactions in size-structured populations

Abstract: Body size is manifestly one of the most important attributes of an organism from an ecological and evolutionary point of view. Size has a predominant influence on an animal's energetic requirements, its potential for resource exploitation, and its susceptibility to natural enemies. A large literature now exists on how physiological, life history, and population parameters scale with body dimensions (24, 131). The ecological literature on species interactions and the structure of animal communities also stresses the importance of body size. Differences in body size are a major means by which species avoid direct overlap in resource use (153), and size-selective predation can be a primary organizing force in some communities (20, 70). Size thus imposes important constraints on the manner in which an organism interacts with its environment and influences the strength, type, and symmetry of interactions with other species (152, 207). Paradoxically, ecologists have virtually ignored the implications of these observations for interactions among species that exhibit size-distributed populations. For instance, it has been often suggested that competing species

Chaos: An Introduction to Dynamical Systems

Abstract: One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.