Time and systems

Abstract

Purpose

To give a mathematical expression of what could be called the internal time of a dynamical system, a time which is different from the external or reference time.

Design/methodology/approach

The paper introduces a general mathematical definition of internal duration and so of internal time. Then we consider the case of an explosion followed by an implosion, which we apply to cosmology and physiology. The case of diffusion is also presented.

Findings

The internal time is generally different from the reference time. In certain cases to a finite reference duration may correspond an infinite internal duration.

Research limitations/implications

Our formulations may help to understand certain aspects of cosmology, physiology and more generally of the evolution of dynamical systems.

Practical implications

For example, the physiology of ageing.

Originality/value

The consideration of the square of the speed of evolution, at instant t, of a dynamical system for measuring the internal duration of interval (t,t+dt) is original, as well as its consequences.

Citation

Vallée, R. (2005), "Time and systems", Kybernetes, Vol. 34 No. 9/10, pp. 1563-1569. https://doi.org/10.1108/03684920510614812