Chaos in biological systems

Abstract

Chaos is a widespread and easily recognizable phenomenon that hardly anybody took notice of until recently. The reason may be that chaos has something profoundly counterintuitive about it. It will not fit easily into any familiar cause–effect frame. The best introduction to chaos is by the way of an example. Consider a leaking faucet (Shaw, 1984). When the weight of the accumulating drop exceeds the surface tension the drop falls and a new drop begins to form. If the leak is small and the pressure in the faucet is constant, the time taken for the drop to reach the critical weight is constant. The dripping is perfectly periodic, the period depending on the leak rate. If the leak is slightly increased, the period of dripping will decrease slightly and vice versa. However, somewhere beyond this point the leaking faucet becomes a nuisance. When the leak is increased beyond a certain point the dripping looses its regularity. The time interval between the drops will first alternate periodically between a short and a long time interval. After a further increase of the leak this double periodic pattern will become unstable and change into a new pattern where four different time intervals between the drops alternate periodically. As the leak is further increased the period will double again and again and finally the dripping becomes completely irregular without any repeating pattern. When this occurs we are observing chaos. At the same time we are posed with the problem of understanding how such a ridiculously simple system can show random behaviour.

Complex dynamics in a carbon-nitrogen model of a grass-legume pasture

“…Additionally we have represented the dynamics of soil organic matter by a simple time delay; in reality, there is a spectrum of time delays in the soil organic matter system, as discussed by Jenkinson (1990), Parton et al (1987), and many others. A time delay increases the tendency towards chaos (Olsen and Degn, 1985). Tentatively, it may be concluded from the current study that the system's sensitivity to parameters is such that it may appear chaotic on time scales ofpractical interest (::::; 10 years), even though it is periodic in the long term for environments and managements that are strictly constant, although these will not occur in practice.…”

Chaos, Fractal in Biology, Biothermodynamics and Matrix Representation on Hypercycle

“…Guevara, et al (1981) researched phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Olsen and Degn (1985) searched chaos in biological systems. Rapp (1993) researched chaos in neurosciences as cautionary tales from the frontiers.…”

Changes in the dynamical behavior of nonlinear systems induced by noise

“…It is known that the incidence of childhood diseases such as chickenpox, measles, mumps and rubella, varies seasonally [98,99]. A standard epidemiological model for the description of these variations, taking into account seasonal variations of the contact rate of children susceptible to infection with infective ones, includes four components: (1) susceptibles (S); (2) exposed but not yet infective (E); (3) infective (I); (4) recovered and immune (R).…”