Skip to Main Content
Mathematical Models for Society and Biology, 2nd Edition
book

Mathematical Models for Society and Biology, 2nd Edition

by Edward Beltrami
June 2013
Intermediate to advanced content levelIntermediate to advanced
288 pages
8h 12m
English
Academic Press
Content preview from Mathematical Models for Society and Biology, 2nd Edition
Appendix C

Nonlinear Differential Equations and Oscillations

In Section 8.3 we discussed systems of linear differential equations of the form x′ = Ax. These are written in vector notation in which A is the matrix of coefficients and the prime ′ indicates differentiation. Our interest in these equations stems from the fact that the local behavior of solutions of a nonlinear system of differential equations x′ = f(x) about some equilibrium solution is determined by the global behavior of the linearized system x′ = Ax, where A now indicates the Jacobean matrix of f.

Suppose x is an equilibrium point of x′ = f(x), with f(x) = 0. If solutions that begin nearby to x return to this point as t increases, we say that the equilibrium is an attractor or, ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Mathematical Modeling in the Social and Life Sciences

Mathematical Modeling in the Social and Life Sciences

Michael Olinick
Illustrated Guide to Home Biology Experiments

Illustrated Guide to Home Biology Experiments

Robert Robert Bruce Thompson Thompson, Barbara Barbara Fritchman Thompson Thompson

Publisher Resources

ISBN: 9780124046245