Darbouxian integrability for polynomial vector fields on the 2-dimensional sphere.
Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system
In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.
Degenerated singular cycles of inclination-flip type
Die Eindeutigkeit des Grenzzyklus bei der Liénardschen Differentialgleichung.
Differential equations with infinite number of limit cycles
Differential growth models for microbial populations
Two models of microbial growth are derived as a resuslt of a discussion of the models of Monod and Hinshelwood types. The approach takes account of the lyse of dead cells in inhibitory products as well as in those which stimulate the growth. The asymptotic behaviour of the models is proved and the models applied to a chemostat.
Dynamic systems described by differential equations with singularities of the type and their machine solving
Dynamical analysis of a demand governed market.