Some global stability results as well as the boundedness of solutions are derived by using a suitably defined Lyapunov functional. We show the existence of both supercritical and subcritical Hopf bifurcations. We demonstrate that the number of all bifurcation diagrams is 8 but that the possible ...
A classical graphical method is easily adapted to carry on the continuation of the oscillatory branches to depict the local bifurcation diagrams. Moreover, several higher-order harmonic balance approximations are implemented to compare the accuracy of the computed solutions. The results are presented ...
A clade is a specific part of the cladogram that includes the recent ancestor and its descendants. It can be indicated by marking out a particular node and all of its associated branches. 4. Branches The branches indicate the bifurcation of the root into nodes. Links between the organisms ...
Some global stability results as well as the boundedness of solutions are derived by using a suitably defined Lyapunovfunctional. We show the existence of both supercritical andsubcritical Hopf bifurcations. We demonstrate that the number of allbifurcation diagrams is 8 but that the possible sequential...
Topological classification of bifurcation sets (separatrices) and phase diagrams of the model are performed. It is shown that there are two critical values of the field: at the smaller value the isostructural phase transition of nematic-paranematic (N-pN) type cannot be realized and at the ...
Here bifurcation diagrams of binary types of Steiner minimal networks for four boundary points are constructed and some properties of such diagrams for any number of points are discussed.doi:10.1007/s10958-021-05658-yE. I. StepanovaSpringer USJournal of mathematical sciences...
We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of ...
In addition, conditions for the persistence of the system are found according to the existence of limit cycles. Some numerical examples are given to substantiate our theoretical results. Moreover, we provide numerical evidence of the existence of chaotic phenomena by illustrating bifurcation diagrams ...
The method is applied to various systems, from Van der Pol and Duffing oscillators to toy models of clarinet and saxophone. The harmonic balance method is ascertained from a comparison to standards time-integration solvers. Bifurcation diagrams are drawn which are sometimes intricate, showing the ...
Then in terms of the bifurcation theory, a detailed qualitative analysis of the system is carried out, and for the bifurcation parameters, their corresponding critical bifurcation values are determined. Combining with the orbits in phase diagrams under different parameters, solitary waves and periodic ...