Limit Cycles of a Class of Polynomial Differential Systems Bifurcating from the Periodic Orbits of a Linear Center

Abstract

In this paper, we study the number of limit cycles of a new class of polynomial differential systems, which is an extended work of two families of differential systems in systems considered earlier. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of a center using the averaging theory of first and second order.

Analysis of a Predator-Prey Model with Distributed Delay

“…We know that x 3 ðtÞ = 0∀t > 0. Then, (6) becomes an ODE model. By Lemma 6 in [9], this lemma is true.…”

“…The predator-prey model of Gauss type is a well-known simple mathematical model describing the interaction between species. Its variations and extensions are studied in modern day population dynamics theory (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). This model is based on the assumption that in real-world ecosystems prey populations do not grow exponentially in the absence of a predator, but rather their size is eventually limited by the absence of resources.…”

On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations

“…e averaging theory is one of the most important tools used actually to the study of limit cycles for second and higher order differential equations, you can see in [2][3][4][5][6][7][8]. More details on the averaging theory can be found in the books of Sanders and Verhulst [9] and of Verhulst [9].…”

On Behavior of the Periodic Orbits of a Hamiltonian System of Bifurcation of Limit Cycles

“…has a long history, where f(x, y) is a polynomial with real coefficients of degree n. Since it was first introduced in Kukles 1944, many researchers have concentrated on its maximum number of limit cycles and their location. See, for example, [3][4][5].…”

“…Theorem 2. Consider system (5) with q � lp, l is a positive integer, and |ε| sufficiently small; let H(n i , l) denote the maximum number of limit cycles of the polynomial differential system (5) bifurcating from the periodic orbits of the center _…”