Paper constructs approximate analytical expressions of periodic disequilibrium fluctuations business cycles occurring in connection with Hopf bifurcations in nonlinear problems of economic interactions described by four-dimensional continuous time dynamical systems. Two nonlinear macrodynamic models are employed as tests models. The region of equilibrium stability in parameter space is obtained...

Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying the onset of an inherent bifurcation, stabilizing a bifurcated solution or branch, changing the parameter value of an existing bifurcation point, modifying the shape or type of a bifurcation chain, int...

By introducing a max-plus dynamical system having limit cycles, we discuss their periodicity, especially the number of discrete states in them. We also find that quasi-periodic cycles exist depending on bifurcation parameter system. Approximate relations between and value are proposed.

In this paper, the problem of bifurcation of limit cycles from degenerate singular point and infinity in a class of septic polynomial differential systems is investigated. Using the computer algebra system Mathematica, the limit cycle configurations of {(8), 3} and {(3), 6} are obtained under synchronous perturbation at degenerate singular point and infinity. To our knowledge, up to now, this i...

Time-periodic vortex flows in an enclosed circular cylinder driven by the rotation of one endwall are investigated experimentally and numerically. This work is motivated partly by the linear stability analysis of Gelfgat et al. J. Fluid Mech. 438, 363 2001 , which showed the existence of an axisymmetric double Hopf bifurcation, and the purpose of the experiment is to see if the nonlinear dynami...

We investigate the bifurcation of small–amplitude limit cycles in generalized Liénard equations. We use the simplicity of the Liénard family, to illustrate the advantages of the approach based on Bautin ideals. Essentially, this Bautin ideal is generated by the so–called Lyapunov quantities, that are computed for generalized Liénard equations and used to detect the presence of a Hopf– Takens bi...

We study the Kaldor-Kalecki model of business cycles with delay in both the gross product and the capital stock. Simple-zero and double-zero singularities are investigated when bifurcation parameters change near certain critical values. By performing center manifold reduction, the normal forms on the center manifold are derived to obtain the bifurcation diagrams of the model such as Hopf, homoc...

We investigate the normal form of a subcritical Hopf bifurcation subjected to time-delayed feedback control. Bifurcation diagrams which cover time-dependent states as well are obtained by analytical means. The computations show that unstable limit cycles with an odd number of positive Floquet exponents can be stabilized by time-delayed feedback control, contrary to incorrect claims in the liter...