Control of Non Linear Oscillations in Plasma Governed by A Van Der Pol Equation

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– Control of Non Linear Oscillations in Plasma Governed by A Van Der Pol Equation –

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Abstract

This thesis deals with the control of non-linear oscillations in plasma governed by a classical Van der Pol equation. The main interest devoted to such an investigation is that non-linear oscillations in plasma are essential in the industry.

In chapter 1, we present some generality on the dynamical systems. Chapter 2 is focused on the analytical study of the Van der Pol equation in the autonomousregime. The amplitude and the phase of the stable limit cycle are derived using the Averaging Method . In chapter 3, we investigate the oscillations in plasma.

Introduction

1.1 Background of the Study

The dynamical systems constitute a very large eld of science [1, 2, 3, 4, 5]. They are generally represented by non-linear equations. A phenomenon is non-linear when his evolution doesn’t obey a linear Mathematics law.

The non-linear electric oscillators are those whom the one of the constitutive elements to the characteristics intensity – tension is of the non-linear form. We can mention (diode, transistor, operational amplier, etc) The presence of the non-linear components is in the beginning of many observed phenomena.

We can also mention (hysteresis, resonance [6, 7]) Another important phenomenon resulting of the presence of non-linear components is the apparition of chaos, curious phenomenon, rich and complex met almost in all branches of instruction: electronic, astronomy, biology, chemistry, economy, etc.

Particularly in electronic, it is known the works of a Dutch electrical engineer Balthazar Van der Pol on an oscillator presenting a various mode[8] whom equation is.

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