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...

Jiang and Niu [12] Gyllenberg et al. [4] showed that nontrivial periodic orbits for three dimensional Ricker competitive system only occur in Jiang-Niu's classes $ 26-31 $. This paper proves 27-31 admit at least limit cycles, possessing two cycles are also provided.

In this paper, we investigate the problem of limit cycles for general Higgins–Selkov systems with degree $$n+1$$ . particular, first prove uniqueness a Liénard system, which allows discontinuity. Then, by changing into systems, theorems and some techniques can be applied. After, nonexistence if bifurcation parameter is outside an open interval. Finally, complete analysis showing its uniqueness.

In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of is Hamiltonian. Under assumption, no more than cycle. This characterizes integrals.

We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems. Our main result shows that three is an upper bound for the number of limit cycles that bifurcate from a center, up to first order expansion of the displacement function. Moreover, this upper bound is reached. The main technique used is the Averaging...