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Friday, May 15, 2020 | History

5 edition of **Integro-Differential Equations and Delay Models in Population Dynamics (Lecture Notes in Biomathematics : 20)** found in the catalog.

Integro-Differential Equations and Delay Models in Population Dynamics (Lecture Notes in Biomathematics : 20)

C. M. Cushing

- 226 Want to read
- 22 Currently reading

Published
**June 1977**
by Springer-Verlag
.

Written in English

The Physical Object | |
---|---|

Number of Pages | 196 |

ID Numbers | |

Open Library | OL7442647M |

ISBN 10 | 0387084495 |

ISBN 10 | 9780387084497 |

"Functional differential equation" is the general name for a number of more specific types of differential equations that are used in numerous applications. There are delay differential equations, integro-differential equations, and so on. Differential difference equation. In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations.

In this paper, we analyze the steady state stability of a model motivated by and previously studied by the author in [].The model is given by an integro-delay differential equation (IDDE) coupled to a partial differential equation (PDE) and is characterized by an exponential “weighting” function that regulates the net repression effect on mRNA based on protein synthesis : Anael Verdugo. Stability and Oscillations in Delay Differential Equations of Population Dynamics Read While You Wait - Get immediate ebook access, if available*, when you order a print book Mathematics Computational Science & Engineering. Mathematics and Its : Springer Netherlands.

the capacitance. The activity of interacting inhibitory and excitatory neurons can be described by a system of integro-differential equations, see for example the Wilson-Cowan model.. Epidemiology. Integro-differential equations have found applications in epidemiology, the mathematical modeling of epidemics, particularly when the models contain age-structure or describe spatial epidemics. Second Order Stochastic Partial Integro Differential Equations with Delay and Impulses M.V.S.S.B.B.K. Sastry Department of Mathematics, UCEK, Impulsive issues can be observed in population dynamics, pharmacokinetics, optimal control framework, economical control sys- memory which arise in biological population models, ecological models Author: M.V.S.S.B.B.K. Sastry, G.V.S.R. Deekshitulu.

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Buy Integro-Differential Equations and Delay Models in Population Dynamics (Lecture Notes in Biomathematics: 20) on FREE SHIPPING on qualified ordersCited by: Integrodifferential Equations and Delay Models in Population Dynamics. Usually dispatched within 3 to 5 business days. These notes are, for the most part, the result of a course I taught at the University of Arizona during the Spring of Their main purpose is to inves tigate the effect that delays (of Volterra integral type) have when placed in the differential models of mathematical ecology, as far as Brand: Springer-Verlag Berlin Heidelberg.

Integrodifferential Equations and Delay Models in Population Dynamics. These notes are, for the most part, the result of a course I taught at the University of Arizona during the Spring of Their main purpose is to inves tigate the effect that delays (of Volterra integral type) have when placed in the differential models of mathematical ecology, as far as stability of equilibria and the Author: J.

Cushing. 2 Predator-Prey Models with Density Terms.- Predator-Prey Models with Response Delays to Resource Limitation.- Stability and Vegetation-Herbivore-Carnivore Systems.- Some Other Delay Predator-Prey Models.- The Stabilization of Predator-Prey Interactions.- A General Predator-Prey Model.- Competition and Mutualism.- Integrodifferential Equations and Delay Models in Population Dynamics.

Authors (view affiliations) Jim M. Cushing; Book. have when placed in the differential models of mathematical ecology, as far as stability of equilibria and the nature of oscillations of species densities are concerned.

Biomathematik Equations Funktional. Get this from a library. Integrodifferential Equations and Delay Models in Population Dynamics. [Jim M Cushing] -- These notes are, for the most part, the result of a course I taught at the University of Arizona during the Spring of Their main purpose is to inves tigate the effect that delays.

Integro-Differential Equations and Delay Models in Population Dynamics (Lecture Notes in Biomathematics: 20) Paperback – 1 June by C. Cushing (Author) See all formats and editions Hide other formats and editionsAuthor: C.

Cushing. Integrodifferential Equations and Delay Models in Population Dynamics, vol. 20, Springer Science & Business Media () Duchateau, M.J. Duchateau Agonistic behaviours in colonies of the bumblebee Bombus terrestrisCited by: Abstract. Integrodifferential equations appear quite early in the mathematical development of theoretical population dynamics in the pioneering work of such mathematicians as V.

Volterra. Epidemic models with delays have received much attention since delays can often cause some complicated dynamical behaviours. Delays in many population dynamics models can destabilise an equilibrium and thus lead to periodic solutions by Hopf bifurcation [21]. Similar results are also obtained for epidemiological models (Brauer.

Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike. Enter your mobile number or email address below and we'll send you a link to download the free Cited by: This led Volterra in particular to include functionals of (Volterra) integral type in what have become the classical differential models of population dynamics and mathematical ecology (equations such as the logistic equation, the famous predator-prey system of Volterra and the well-known Volterra-Lotka competition model).Cited by: 3.

Periodic Delay Models Integrodiﬀerential Equations 11 State-Dependent Delays 12 Diﬀusive Models with Delay Fisher Equation Diﬀusive Equations with Delay 12 Well-Posedness, Regularity and Asymptotic Behaviour of Re-tarded Diﬀerential Equations by Extrapolation Theory L.

Maniar 1. J.M. Cushing, "Integrodifferential equations and delay models in population dynamics", Springer () [a3] H. Grabmüller, "Singular perturbation techniques applied to integro-differential equations". Population equilibria of Daphnia and Ceriodaphnia in a chain of semi-chemostats Predicted and observed equilibrium values of algae in the presence of Daphnia Population dynamics of the snowshoe hare and the lynx in northern Canada Population dynamics of two species of voles in northern Finland Full text access 5 Periodic Solutions, Chaos, Structured Single Species Models Pages Download PDF.

Integrodifferential equations and delay models in population dynamics [] Cushing, J. (James M.) Access the full textCited by: An explicit finite difference algorithm is developed to approximate the solution of a nonlinear and nonlocal system of integro-differential equations that models the dynamics of a two-sex population.

The algorithm is unconditionally stable. The optimal rate of convergence of the algorithm is demonstrated for the maximum norm. Results from a numerical simulation of U.S. population growth from Cited by: Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems.

The book treats both autonomous and nonautonomous systems with various delays. Key topics addressed are the possible delay influence on the dynamics of the system, such as stability switching as time delay increases, the long time coexistence of. of delay eﬀects in the population dynamics of many species.

Basic Properties of Delay Diﬀerential Equations While similar in appearance to ordinary diﬀerential equations, delay diﬀerential equations have several features which make their analysis more complicated.

Let us examine an example of the form () ˙x(t) = f(x(t),x(t−τ)).Cited by:. Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathemat Springer, Berlin Heidelberg New York, originally published in and reprinted inISBN On fractional integro-differential equations with state-dependent delay Article in Computers & Mathematics with Applications 62(3) August with 31 Reads How we measure 'reads'.An integro-differential reaction-diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase.

It is claimed that this is inherently more realistic than the usual kind of reaction-diffusion model for mobile populations. Three kinds of bifurcation from the uniform steady-state solution Cited by: