Oscillations were first studied as part of nonlinear mechanics and a long standing and comprehensive literature exists. In particular, there are fundamental theories concerning the existence of stable periodic solutions. Some knowledge of this mathematical background is helpful in interpreting the results of nonlinear system analyses. Conversely, if it is required to construct a mathematical model of a stable periodic system, such as a biological oscillator, it will be essential to postulate a mechanism that has the necessary properties.

Inspec keywords: oscillations; periodic control; stability; nonlinear dynamical systems

Other keywords: nonlinear system analyses; biological oscillator; stable periodic solutions; limit cycles; relaxation oscillations; nonlinear mechanics

Subjects: Nonlinear control systems