This was also predicted by numerical solutions to the equations of the model. Four population cages of houseflies maintained for periods up to 2. The populations fluctuated markedly and regularly in adult size, generally between and 1,, with a periodicity of 5—6 wk. The correspondence between prediction and observation was reasonably close and was improved when further complications were considered and the behavior of the populations was simulated on a computer. In another cage maintained under different conditions of husbandry, where oviposition was less but other parameters were the same, the stability and population size differed in a manner predicted by the model.
Of several theories that might explain oscillations, only that of time delays is likely to be appropriate for these populations. Volume 57 , Issue 5. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username. Become a Member ESA.
Delay Differential Equations: Theory, Application and Oscillation
Ecology Volume 57, Issue 5. Charles E. Taylor Search for more papers by this author. Robert R. Sokal Search for more papers by this author. Tools Request permission Export citation Add to favorites Track citation. Share Give access Share full text access. Share full text access.
Please review our Terms and Conditions of Use and check box below to share full-text version of article. Abstract Oscillations of animal population size can be caused by time delays due to development.
Differential Equations: Stability, Oscillations, Time Lags - Google книги
Citing Literature. For instance, consider the DDE with a single delay. This can be continued for the successive intervals by using the solution to the previous interval as inhomogeneous term. In practice, the initial value problem is often solved numerically.
Then the initial value problem can be solved with integration,. In some cases, differential equation can be represented in a format that looks like a delay differential equations. Because of the exponential in the characteristic equation, the DDE has, unlike the ODE case, an infinite number of eigenvalues, making a spectral analysis more involved.
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The spectrum does however have some properties which can be exploited in the analysis. For instance, even though there are an infinite number of eigenvalues, there are only a finite number of eigenvalues to the right of any vertical line in the complex plane. This characteristic equation is a nonlinear eigenproblem and there are many methods to compute the spectrum numerically.
Consider, for example, the following DDE:. From Wikipedia, the free encyclopedia.
Differential equations Navier—Stokes differential equations used to simulate airflow around an obstruction. Natural sciences Engineering. Order Operator.
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Relation to processes. Difference discrete analogue Stochastic Stochastic partial Delay. General topics. Phase portrait Phase space. Numerical integration Dirac delta function. Solution methods. Masters Theses. Retrieved Bellman, Richard; Cooke, Kenneth L. Differential-difference equations. New York-London: Academic Press. Driver, Rodney D. Ordinary and Delay Differential Equations.