Criteria on the existence of limit cycles in planar polynomial differential systems

Upper Bounds for the Number of Limit Cycles of Some Planar Polynomial Differential Systems

We give an effective method for controlling the maximum number of limit cycles of some planar polynomial systems. It is based on a suitable choice of a Dulac function and the application of the well-known Bendixson-Dulac Criterion for multiple connected regions. The key point is a new approach to control the sign of the functions involved in the criterion. The method is applied to several examp...

Existence and Uniqueness of Limit Cycles in a Class of Planar Differential Systems

On the Existence and Uniqueness of Limit Cycles in Planar Piecewise Linear Systems without Symmetry

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter pro...

Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11

In this article, a systematic procedure has been explored to studying general Zq-equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z12-equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-...

Limit Cycles of Planar Quadratic Differential Equations

Since Hilbert posed the problem of systematically counting and locating lhe limit cycle of polynomial systems on the plane in 1900, much ef Tort has been expended in its investigation. A large body of literature chiefly by Chinese and Soviet authors has addressed this question in the context of differential equations whose field is specified by quadratic polynomials, In this paper we consider t...