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Limit Cycles of Differential Equations
This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de...
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Chapter 1 Centers and Limit Cycles
In this chapter I want to give a general background to the center-focus problem, and then to show why the problem is interesting: both in what it...
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Chapter 2 Abelian Integrals and Limit Cycles
In this chapter we will explain the relation between the number of zeros of the Abelian integrals and the number of limit cycles of the corresponding...
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On Stability Discrimination of Limit Cycles for Piecewise Smooth Systems
This paper is concerned with the problem of stability discrimination of limit cycles for piecewise smooth systems. We first establish the Poincaré...
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Chemical Systems with Limit Cycles
The dynamics of a chemical reaction network (CRN) is often modeled under the assumption of mass action kinetics by a system of ordinary differential...
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The limit cycles of a class of piecewise differential systems
In this century many papers have been published on the piecewise differential systems in the plane. The increasing interest for this class of...
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On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields
It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytic vector fields. In the polynomial...
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Limit Cycles in Discontinuous Planar Piecewise Differential Systems with Multiple Nonlinear Switching Curves
In this paper, we investigate the maximum number of limit cycles that can bifurcate from the periodic annulus of the linear center for discontinuous...
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Limit Cycles of Continuous Piecewise Smooth Differential Systems
From the beginning of this century many articles have been published on the continuous and discontinuous piecewise differential systems specially in...
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Limit cycles of polynomial differential systems of degree 1 and 2 on the cylinder
We consider planar polynomial differential systems of degree 1 and 2 on the cylinder and we study their limit cycles. We prove that such linear...
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Four Limit Cycles for a Rock-Scissor-Paper Game Between Bacteriocin Producing Bacteria
In this paper, four limit cycles are constructed for a concrete 3D model of rock-scissor-paper (RSP) game between bacteriocin producing bacteria....
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Nine Limit Cycles Around a Weak Focus in a Class of Three-Dimensional Cubic Kukles Systems
In this paper, we study the bifurcation of limit cycles, centers, and isochronous centers for a class of three-dimensional Kukles systems of degree...
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Limit Cycles of Discontinuous Piecewise Differential Systems Formed by Linear and Cubic Centers via Averaging Theory
Finding the number of limit cycles, as described by Poincaré (Memoire sur les coubes definies par une equation differentielle, Editions Jacques...
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Multiplicity on Limit Cycles of 3D Lotka-Volterra Competitive Systems
In the existing literatures, there exist at least four limit cycles for 3D Lotka-Volterra competitive systems in Zeeman’s classes 26 and 27 with no...
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Number of Limit Cycles for Planar Systems with Invariant Algebraic Curves
For planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We...
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Truly Nonlinear Oscillator with Limit Cycles and Harmonic Solutions
This paper presents some classes of truly nonlinear oscillatory equations of polynomial type. It has been shown that these classes can generate many...
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Four crossing limit cycles of a family of discontinuous piecewise linear systems with three zones separated by two parallel straight lines
In this paper, we study the maximum number of limit cycles that can exhibit a planar discontinuous piecewise differential system separated by two...
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