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Maoan Han

Publications and source records attributed to Maoan Han.

7 recordsLinked to original sources
arXiv2025

Determining codimension of Bogdanov-Takens and Bautin bifurcations via simplest normal form computation

In solving real-world problems, determining the codimension of Bogdanov-Takens (BT) and Bautin (generalized Hopf) bifurcations can be very challenging, even for simple two-dimensional dynamical systems. This difficulty becomes particularly evident when the number of system parameters exceeds the codimension of the bifurcations. Such challenges are closely linked to analyzing complex dynamics, such as the bifurcation of multiple limit cycles and homoclinic/heteroclinic bifurcations. In this paper, we use two population systems to demonstrate a systematic approach for determining the conditions that define the codimension of BT and Bautin bifurcations.

math.DS↗
arXiv2022

An efficient solution procedure for solving higher-codimension Hopf and Bogdanov-Takens bifurcations

In solving real world systems for higher-codimension bifurcation problems, one often faces the difficulty in computing the normal form or the focus values associated with generalized Hopf bifurcation, and the normal form with unfolding for higher-codimension Bogdanov-Takens bifurcation. The difficulty is not only coming from the teadious symbolic computation of focus values, but also due to the restriction on the system parameters, which frequently leads to failure of the conventional approach used in the computation even for simple $2$-dimensional nonlinear dynamical systems. In this paper, we use a simple 2-dimensional epidemic model, for which the conventional approach fails in analyzing the stability of limit cycles arising from Hopf bifurcation, to illustrate how our method can be efficiently applied to determine the codimension of Hopf bifurcation. Further, we apply the simplest normal form theory to consider codimension-3 Bogdanov-Takens bifurcation and present an efficient one-step transformation approach, compared with the classical six-step transformation approach to demonstrate the advantage of our method.

math.DS↗
arXiv2011

Bifurcations of planar Hamiltonian systems with impulsive perturbation

In this paper, by means of the Melnikov functions we consider bifurcations of harmonic or subharmonic solutions from a periodic solution of a planar Hamiltonian system under impulsive perturbation. We give some sufficient conditions under which a harmonic or subharmonic solution exists.

math.CA↗
arXiv2011

On the number of limit cycles of polynomial Lienard systems

Lienard systems are very important mathematical models describing oscillatory processes arising in applied sciences. In this paper, we study polynomial Lienard systems of arbitrary degree on the plane, and develop a new method to obtain a lower bound of the maximal number of limit cycles. Using the method and basing on some known results for lower degree we obtain new estimations of the number of limit cycles in the systems which greatly improve existing results.

math.CA↗
arXiv2011

Limit cycle bifurcations from a nilpotent focus or center of planar systems

In this paper, we study the analytical property of the Poincare return map and the generalized focal values of an analytical planar system with a nilpotent focus or center. Then we use the focal values and the map to study the number of limit cycles of this kind of systems with parameters, and obtain some new results on the lower and upper bounds of the maximal number of limit cycles near the nilpotent focus or center.

math.CA↗
arXiv2010

Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials

In this paper, we give a positive answer to the open question: Can there exist 4 limit cycles in quadratic near-integrable polynomial systems? It is shown that when a quadratic integrable system has two centers and is perturbed by quadratic polynomials, it can generate at least 4 limit cycles with (3,1) distribution. The method of Melnikov function is used.

math.DS↗