# ON SECOND ORDER BIFURCATIONS OF LIMIT CYCLES

## Related Articles

- A POINCARÃ‰ BIFURCATION OF A CLASS OF HAMILTONIAN SYSTEM WITH CUBIC SOLUTIONS DISTURBED BY A CUBIC POLYNOMIAL. Chengbin Si; Yonghong Ren // Far East Journal of Applied Mathematics;Dec2013, Vol. 85 Issue 1/2, p1
The cubic function H(x, y) = xy2 + 2ey - x2 - (2 + e2 ) x - (1 + 2e2 ) = h is a Hamiltonian function of the following system: áº‹ = 2xy + 2e, áº = (2 + e2 ) + 2x - y2, which can be bifurcated out at least four limit cycles after a cubic polynomial disturbance, i.e., B(2, 3) â‰¥ 4.

- DNS Curves in a Production/Inventory Model. Feichtinger, G.; Steindl, A. // Journal of Optimization Theory & Applications;Feb2006, Vol. 128 Issue 2, p295
In this paper, we investigate the bifurcation behavior of an inventory/production model close to a Hamilton-Hopf bifurcation. We show numerically that two different types of DNS curves occur: If the initial states are far from the bifurcating limit cycle, the limit cycle can be approached along...

- EVALUATING CYCLICITY OF CUBIC SYSTEMS WITH ALGORITHMS OF COMPUTATIONAL ALGEBRA. Levandovskyy, Viktor; Pfister, Gerhard; Romanovski, Valery G. // Communications on Pure & Applied Analysis;Sep2012, Vol. 11 Issue 5, p2029
We describe an algorithmic approach to studying limit cycle bifurcations in a neighborhood of an elementary center or focus of a polynomial system. Using it we obtain an upper bound for cyclicity of a family of cubic systems. Then using a theorem by Christopher [3] we study bifurcation of limit...

- Bifurcation in the stable manifold of the bioreactor with nth and mth order polynomial yields. Xuncheng Huang; Lemin Zhu // Journal of Mathematical Chemistry;Jul2009, Vol. 46 Issue 1, p199
The three dimensional chemostat with nth and mth order polynomial yields, instead of the particular one such as A + BS, A + BS2, A + BS3, A + BS4, A + BS2 + CS3 and A + BS n, is proposed. The existence of limit cycles in the two-dimensional stable manifold, the Hopf bifurcation and the stability...

- Dulac-Cherkas function in a neighborhood of a structurally unstable focus of an autonomous polynomial system on the plane. Grin', A. // Differential Equations;Jan2014, Vol. 50 Issue 1, p1
We consider the problem of estimating the number of limit cycles and their localization for an autonomous polynomial system on the plane with fixed real coefficients and with a small parameter. At the origin, the system has a structurally unstable focus whose first Lyapunov focal quantity is...

- The Number of Limit Cycles of a Polynomial System on the Plane. Chao Liu; Maoan Han // Abstract & Applied Analysis;2013, p1
We perturb the vector field x = -yC(x, y), y = xC(X, Y) with a polynomial perturbation of degree n, where C(x, y) = (1 - y2)m, and study the number of limit cycles bifurcating from the period annulus surrounding the origin.

- CENTRES AND LIMIT CYCLES FOR AN EXTENDED KUKLES SYSTEM. Hill, Joe M.; Lloyd, Noel G.; Pearson, Jane M. // Electronic Journal of Differential Equations;2007, Vol. 2007, p1
We present conditions for the origin to be a centre for a class of cubic systems. Some of the centre conditions are determined by finding complicated invariant functions. We also investigate the coexistence of fine foci and the simultaneous bifurcation of limit cycles from them.

- Limit Cycle Bifurcations in a Class of Cubic System near a Nilpotent Center. Jiao Jiang // Applied Mathematics;Jul2012, Vol. 3 Issue 7, p772
In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.

- Bifurcations of limit cycles from a quintic Hamiltonian system with a heteroclinic cycle. Zhao, Li; Li, De // Acta Mathematica Sinica;Mar2014, Vol. 30 Issue 3, p411
In this paper, we consider LiÃ©nard systems of the form where b âˆˆ â„, 0 < |âˆˆ| â‰ª 1, ( Î±, Î², Î³) âˆˆ D âˆˆ â„ and D is bounded. We prove that for | b| â‰« 1 ( b < 0) the least upper bound of the number of isolated zeros of the related Abelian integrals...