Limit Cycles
Limit cycles in a Kolmogorov type model
... The stability of equilibrium points, the existence and uniqueness of limit cycles in the model are proved... KEY WORDS AND PHRASES.[r] ...
12
Bifurcation of limit cycles at degenerate singular point and infinity in a septic system
... of limit cycles from the origin and infinity under synchronous perturbation: [] obtained the limit cycle configurations of { (), } and {(), } in a cubic polynomial differential system; [] and ...
10
Limit Cycles of a Class of Hilbert's Sixteenth Problem Presented by Fractional Differential Equations
... The second part of the well-known Hilbert’s 16th problem is still unsolved since Hilbert proposed it in 1900. This problem is concerned with the maximum number of limit cycles and their relative ...
12
Bifurcations of limit cycles in a reduced model of the Xenopus tadpole central pattern generator
... of limit cycles corresponding to swimming and ...unstable limit cy- cles, which should be also included into consideration for clarity of the multiple interlinked ...unstable cycles are shown ...
31
Limit cycles in a quartic system with a third order nilpotent singular point
... of limit cycles, which is different from the first kind of bifurcation discussed in previous section, will be ...amplitude limit cycles near the origin can be ...
15
Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
... have limit cycles, then must limit cycles contained in the set { ( , ) 0} V ρ θ = ...possible limit cycles must be given by ...
8
Computing Regions of Stability for Limit Cycles of Piecewise Affine Systems
... By using the impact map, i.e., the map from one switching surface to the next switching surface, Gonçalves analyzed both global and local stabilities of limit cycles [3]-[6]. The solution was computed by ...
11
Limit cycles for perturbing Hamiltonian system inside piecewise smooth polynomial differential system
... of limit cycles for perturbing the global center and truncated pendulum inside a piecewise smooth cubic polynomial differential ...more limit cycles than the smooth ...
8
Bifurcation of Limit Cycles in Smooth and Non-smooth Dynamical Systems with Normal Form Computation
... 1990’s, Ilyashenko and Yakovenko [2], and ´ Ecalle [3] independently proved that H(n) is finite for given planar polynomial vector fields. For general quadratic polynomial systems, the best result is H(2) ≥ 4, obtained ...
153
Bifurcation of limit cycles from a hyper elliptic Hamiltonian system with a double heteroclinic loops
... 4. Han, M, Li, JB: Lower bounds for the Hilbert number of polynomial systems. J. Differ. Equ. 252, 3278-3304 (2012) 5. Dumortier, F, Rousseau, C: Cubic Liénard equations with linear damping. Nonlinearity 3, 1015-1039 ...
11
Local bifurcation of limit cycles and center problem for a class of quintic nilpotent systems
... of limit cycles that appear from it by small perturbations of the coefficients of the given differential equation inside the family considered (see [11] for cases where this relation does not ...produce ...
13
Co Existence of Local Limit Cycles from Degenerate and Weak Foci in Cubic Systems
... local limit cycles of this system, we build a Liapunov function in the fashion outlined in Blows [2], an extension of a result developed by Andreev, Sadovskii, How to cite this paper: Schoonover, ...
7
Limit cycles for discontinuous quadratic differential switching systems
... nine limit cy- cles []. These examples show that there exist more limit cycles in switching systems than continuous systems, and the dynamics of these systems is more ... limit ...
8
Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems
... stable limit cycles surrounding an unstable fixed point, and hence might be interpreted as stylized business or growth ...these limit cycles, therefore, requires a test for both non-degeneracy ...
21
Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems
... the limit cycles emerging from this bifurcation, we reduce our dynamical system represented by (1) to its topological normal form, us- ing a method outlined by (Edneral 2007), (Wiggins 1990) and (Kuznetsov ...
22
Existence of limit cycles in a predator prey system with a functional response
... Abstract. We consider the existence of limit cycles for a predator-prey system with a functional response. The system has two or more parameters that represent the intrinsic rate of the predator population. ...
9
On the non-existence of limit cycles for a class of Kolmogorov systems
... a limit cycle of system (1) is an isolated periodic orbit in the set of all periodic orbits of system ...about limit cycles, most of them deal essentially with their detection, their number and their ...
8
On the existence and the number of limit cycles in evolutionary games
... limit cycles in this model allows us to tackle a number of evolutionary games in which the system (1) is a general case. Particular versions of this system may arise as the outcome of dynamic replicator of ...
17
Local bifurcation of limit cycles and integrability of a class of nilpotent systems
... computer algebra system MATHEMATICA, the first 13 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The result that there exist 13 small ...
11
Limit cycles for planar differential systems with quasi-homogeneous nonlinearities
... the limit cycles of the planar differential systems of (p, q)−quasi- homogeneous polynomials ...two limit cycles by introducing a new form of ...
7