Biomedical subjects

Y A Kuznetsov

Publications and source records attributed to Y A Kuznetsov.

2 recordsLinked to original sources

PubMed1996

Remarks on food chain dynamics.

The main modes of behavior of a food chain model composed of logistic prey and Holling type II predator and superpredator are discussed in this paper. The study is carried out through bifurcation analysis, alternating between a normal form approach and numerical continuation. The two-parameter bifurcation diagram of the model contains Hopf, fold, and transcritical bifurcation curves of equilibria as well as flip, fold, and transcritical bifurcation curves of limit cycles. The appearance of chaos in the model is proved to be related to a Hopf bifurcation and a degenerate homoclinic bifurcation in the prey-predator subsystem. The boundary of the chaotic region is shown to have a very peculiar structure.

Animals↗

PubMed1994

Bifurcation analysis pf periodic SEIR and SIR epidemic models.

The bifurcations of the periodic solutions of SEIR and SIR epidemic models with sinusoidally varying contact rate are investigated. The analysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding portraits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips and cusps) are detected, and multiple stable modes of behavior are identified in various regions of the parameter space. Finally, it is shown how the parametric portrait of the SEIR model tends to that of the SIR model when the latent period tends to zero.

Data Interpretation, Statistical↗