How Long to Read Time Lags in Biological Models

How Long Does it Take to Read Time Lags in Biological Models?

It takes the average reader 1 hour and 55 minutes to read Time Lags in Biological Models by N. MacDonald

Assuming a reading speed of 250 words per minute. Learn more

Description

In many biological models it is necessary to allow the rates of change of the variables to depend on the past history, rather than only the current values, of the variables. The models may require discrete lags, with the use of delay-differential equations, or distributed lags, with the use of integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the techniques available for studying the solution of the equations. A large proportion of the material presented relates to a special method that can be applied to a particular class of distributed lags. This method uses an extended set of ordinary differential equations. I examine the local stability of equilibrium points, and the existence and frequency of periodic solutions. I discuss the qualitative effects of lags, and how these differ according to the choice of discrete or distributed lag. The models studied are drawn from the population dynamiCS of single species (logistic growth, the chemostat) and of interacting pairs of species (predation, mutualism), from cell population dynamiCS (haemopoiesis) and from biochemical kinetics (the Goodwin oscillator). The last chapter is devoted to a population model employing difference equations. All these models include non-linear terms.

How long is Time Lags in Biological Models?

Time Lags in Biological Models by N. MacDonald is 114 pages long, and a total of 28,956 words.

This makes it 38% the length of the average book. It also has 35% more words than the average book.

How Long Does it Take to Read Time Lags in Biological Models Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 38 minutes to read Time Lags in Biological Models aloud.

What Reading Level is Time Lags in Biological Models?

Time Lags in Biological Models is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Time Lags in Biological Models?

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