This paper discusses the bifurcation theory for the equations for traveling surface water waves, based on the formulation of Zakharov [58] and of Craig and Sulem [15] in terms of integro-differential equations on the free surface. This theory recovers the well-known picture of bifurcation curves of Stokes progressive wavetrains in two-dimensions, with the bifurcation parameter being the phase v...

We consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and monotone decreasing branches. It is associated with a credit cycle model introduced by Matsuyama, under the assumption of the Cobb-Douglas production function. We offer a detailed analysis of the dynamics of this family. In particular, using the skew tent map as a border collision normal form w...

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semiclassical app...

In this paper, a predator-prey relationship in the presence of prey refuge was studied. The analysis dependence locally stable equilibrium points on parameters problem carried out. Bifurcation and limit cycles for model were analyzed to show dynamical behaviour system. results showed that system is at constant m = 0.3 harvesting rate H 0.3. However, increasing decreasing or vice versa, remains ...

In this paper, we study the existence of periodic orbits bifurcating from stationary solutions in a non-smooth planar dynamical system. This phenomenon is interpreted as generalized Hopf bifurcation. In the case of smoothness, Hopf bifurcation is characterized by a pair of complex conjugate eigenvalues crossing through the pure imaginary axis. This method does not apply to a non-smooth system d...

The extended Gross-Pitaevskii equation for the Bose-Einstein condensation of gases with attractive 1 /r interaction has a second solution which is born together with the ground state in a tangent bifurcation. At the bifurcation point both states coalesce, i.e., the energies and the wave functions are identical. We investigate the bifurcation point in the context of exceptional points, a phenome...

The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obt...

This paper deals with an SIR model age structure of infected individuals. We formulate the as abstract non-densely defined Cauchy problem and derive conditions for existence all feasible equilibrium points system. The criteria both stability instability involving system parameters are obtained. Bifurcation analysis indicates that exhibits Hopf bifurcation which is main result this paper. Finall...

We investigate the dynamics and transitions to extinction of hypercycles governed by periodic orbits. For a large enough number of hypercycle species (n>4) the existence of a stable periodic orbit has been previously described, showing an apparent coincidence of the vanishing of the periodic orbit with the value of the replication quality factor Q where two unstable (non-zero) equilibrium point...

Kurata, Yasutaka, Ichiro Hisatome, Sunao Imanishi, and Toshishige Shibamoto. Roles of L-type Ca2 and delayed-rectifier K currents in sinoatrial node pacemaking: insights from stability and bifurcation analyses of a mathematical model. Am J Physiol Heart Circ Physiol 285: H2804–H2819, 2003. First published August 14, 2003; 10.1152/ajpheart.01050.2002.—To elucidate the dynamical mechanisms of the...