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.