The Vector Field: Multipliers and Combinations

Mike R. Jeffrey
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Mike R. Jeffrey: University of Bristol, Department of Engineering Mathematics

Chapter Chapter 3 in Hidden Dynamics, 2018, pp 61-72 from Springer

Abstract: Abstract Consider a set of ordinary differential equations d x 1 d t = f 1 ( x 1 , x 2 , … , x n ) , d x 2 d t = f 2 ( x 1 , x 2 , … , x n ) , … e t c . $$\displaystyle{\frac{dx_{1}} {dt} = f_{1}(x_{1},x_{2},\ldots,x_{n})\;,\quad \frac{dx_{2}} {dt} = f_{2}(x_{1},x_{2},\ldots,x_{n})\;,\quad \ldots \quad etc.}$$ or more concisely collecting the state variables x i into an n-dimensional vector x = (x 1, x 2, …, x n), and the functions f i into a vector f = (f 1, f 2, …, f n), with the derivative with respect to time t denoted by a dot.

Date: 2018
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DOI: 10.1007/978-3-030-02107-8_3

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