Dissipative Nambu systems and oscillator circuit design

Abstract

Electronic oscillators have to be described by nonlinear differential equations with a limit cycle where analytical solutions are rarely predictable. Therefore, design concepts of oscillators are not available where a designer can start with a complete set of specifications of the desired oscillator. Only linear aspects of the oscillator design can be solved in a reasonable manner. In this paper we present a mathematical concept that is appropriate to construction nonlinear differential equations with a limit cycle. For this purpose we use a concept from theoretical physics, the so-called Nambu mechanics, and add canonical dissipation. It can be shown that a limit cycle arises under certain conditions. Based on the corresponding system of differential equations a SIMULINK model is constructed that can be the basis of a circuit realization.

Active and Purely Dissipative Nambu Systems in General Thermostatistical Settings Described by Nonlinear Partial Differential Equations Involving Generalized Entropy Measures

“…In fact, for the migration (cell motion) of certain bacteria, experimental evidence has been found that the bacteria velocity scores are distributed in a certain range according to a power law [63]. It has further been suggested that the absolute velocity scores satisfy a Tsallis distribution similar to the power law distribution (29). In short, while a stochastic model of the form (9) may not be able to provide a mechanistic account of the many interacting components of a biological system under consideration, the model might be used as a phenomenological model to address certain macroscopic aspects of the system.…”