Non-Linear Differential Equations and Dynamical Systems

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Synopsis

 
Non-Linear Differential Equations and Dynamical Systems is the second book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This second book consists of two chapters (chapters 3 and 4 of the set).

The first chapter considers non-linear differential equations of first order, including variable
coefficients. A first-order differential equation is equivalent to a first-order differential in two variables.
The differentials of order higher than the first and with more than two variables are also considered.
The applications include the representation of vector fields by potentials.

The second chapter in the book starts with linear oscillators with coefficients varying with time,
including parametric resonance. It proceeds to non-linear oscillators including non-linear resonance,
amplitude jumps, and hysteresis. The non-linear restoring and friction forces also apply to
electromechanical dynamos. These are examples of dynamical systems with bifurcations that may lead
to chaotic motions.



Presents general first-order differential equations including non-linear like the Ricatti equation


Discusses differentials of the first or higher order in two or more variables


Includes discretization of differential equations as finite difference equations


Describes parametric resonance of linear time dependent oscillators specified by the Mathieu functions and other methods


Examines non-linear oscillations and damping of dynamical systems including bifurcations and chaotic motions

Book details

Series:
Mathematics and Physics for Science and Technology
Author:
Luis Manuel Braga da Costa Campos
ISBN:
9780429639616
Related ISBNs:
9780429028991, 9780367137199
Publisher:
CRC Press
Pages:
283
Reading age:
Not specified
Includes images:
Yes
Date of addition:
2022-08-05
Usage restrictions:
Copyright
Copyright date:
2019
Copyright by:
Taylor 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Medicine, Nonfiction, Science, Technology