Biomedical subjects

A Wikan

Publications and source records attributed to A Wikan.

4 recordsLinked to original sources

PubMed2004

On synchronization in semelparous populations.

Synchronization, i.e., convergence towards a dynamical state where the whole population is in one age class, is a characteristic feature of some population models with semelparity. We prove some rigorous results on this, for a simple class of nonlinear one- population models with age structure and semelparity: (i) the survival probabilities are assumed constant, and (ii) only the last age class is reproducing (semelparity), with fecundity decreasing with total population. For this model we prove: (a) The synchronized, or Single Year Class (SYC), dynamical state is always attracting. (b) The coexistence equilibrium is often unstable; we state and prove simple results on this. (c) We describe dynamical states with some, but not all, age classes populated, which we call Multiple Year Class (MYC) patterns, and we prove results extending (a) and (b) into these patterns.

Animals↗

PubMed2001

From chaos to chaos. An analysis of a discrete age-structured prey-predator model.

Discrete age-structured density-dependent one-population models and discrete age-structured density-dependent prey-predator models are considered. Regarding the former, we present formal proofs of the nature of bifurcations involved as well as presenting some new results about the dynamics in unstable and chaotic parameter regions. Regarding the latter, we show that increased predation may act both as a stabilizing and a destabilizing effect. Moreover, we find that possible periodic dynamics of low period, either exact or approximate, may not be generated by the predator, but it may be generated by the prey. Finally, what is most interesting from the biological point of view, is that given that the prey, in absence of the predator, exhibits periodic or almost periodic oscillations of low period, then the introduction of the predator does not alter this periodicity in any substantial way until the stabilizing effect of increased predation becomes so strong that a stable equilibrium is achieved.

Aging↗

PubMed1998

Four-Periodicity in Leslie Matrix Models with Density Dependent Survival Probabilities.

Leslie matrix models with a wide range of density dependent survival probability functions pi are studied. It is shown that for all pi which lead to nonstationary behavior, the instability is introduced through a supercritical Hopf bifurcation and further, that the dynamics in the unstable parameter regions in most cases has a strong resemblance of 4-cycles, either exact or approximate. Even in the chaotic regime a qualitative character of 4-cycles is preserved. Copyright 1998 Academic Press.

Journal Article↗

PubMed1997

Dynamic consequences of reproductive delay in Leslie matrix models with nonlinear survival probabilities.

The dynamic consequences of reproductive delay in Leslie matrix models with nonlinear survival probabilities p are analyzed. In consideration of two-age classes, proof is presented for a wide range of p functions that, outside the strongly resonant cases, the transfer from stability to instability goes through a supercritical Hopf bifurcation and, moreover, that the nonlinear development has a strong resemblance of three or four cycles, either exact or approximate. In three-age class models, the tendency toward four-periodical dynamics is shown to be even more pronounced, a qualitative finding that gradually disappears as we turn to the higher-dimensional cases. We also prove that for models of any dimension n > 1 theme are regions in parameter space where the equilibrium is unstable at its creation and we demonstrate that the dynamics in this age-class extinguishing case is 2k.n cyclic.

Age Factors↗