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Start Over Subject limit cycle

1. Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four

Creator:
Sáez, Eduardo, Stange, Eduardo, and Szántó, Iván
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
stability, limit cycle, center, and bifurcation
Language:
English
Description:
A class of degree four differential systems that have an invariant conic $ x^2+Cy^2=1$, $C\in {\mathbb{R}}$, is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Intuitionistic fuzzy Hopfield neural network and its stability

Creator:
Li, Long, Yang , Jie, and Wu, Wei
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Intuitionistic fuzzy sets, intuitionistic fuzzy Hopfield neural network, limit cycle, stable point, and Lyapunov stability
Language:
English
Description:
Intuitionistic fuzzy sets (IFSs) are generalization of fuzzy sets by adding an additional attribute parameter called non-membership degree. In this paper, a max-min intuitionistic fuzzy Hopfield neural network (IFHNN) is proposed by combining IFSs with Hopfield neural networks. The stability of IFHNN is investigated. It is shown that for any given weight matrix and any given initial intuitionistic fuzzy pattern, the iteration process of IFHNN converges to a limit cycle. Furthermore, under suitable extra conditions, it converges to a stable point within finite iterations. Finally, a kind of Lyapunov stability of the stable points of IFHNN is proved, which means that if the initial state of the network is close enough to a stable point, then the network states will remain in a small neighborhood of the stable point. These stability results indicate the convergence of memory process of IFHNN. A numerical example is also provided to show the effectiveness of the Lyapunov stability of IFHNN.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. On the number of limit cycles of a generalized Abel equation

Creator:
Naeem and Torres, Pedro J.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
periodic solution, limit cycle, and polynomial nonlinearity
Language:
English
Description:
New results are proved on the maximum number of isolated $T$-periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. The existence of limit cycle for perturbed bilinear systems

Creator:
Damak, Hanen, Hammami, Mohamed Ali, and Sun, Yeong-Jeu
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
perturbed bilinear system, feedback control, and limit cycle
Language:
English
Description:
In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the "smallness" of the perturbation parameter ε to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for this class of nonlinear control systems.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public