scholarly journals Gevrey estimates for one dimensional parabolic invariant manifolds of non-hyperbolic fixed points

2017 ◽  
Vol 37 (8) ◽  
pp. 4159-4190 ◽  
Author(s):  
Inmaculada Baldomá ◽  
◽  
Ernest Fontich ◽  
Pau Martín ◽  
◽  
...  
Keyword(s):  
Fixed Points ◽  
Invariant Manifolds ◽  
One Dimensional ◽  
Hyperbolic Fixed Points ◽  
Gevrey Estimates

scholarly journals The parameterization method for one- dimensional invariant manifolds of higher dimensional parabolic fixed points

2007 ◽  
Vol 17 (4) ◽  
pp. 835-865 ◽  
Author(s):  
Inmaculada Baldomá ◽  
◽  
Ernest Fontich ◽  
Rafael de la Llave ◽  
Pau Martín ◽  
...  
Keyword(s):  
Fixed Points ◽  
Invariant Manifolds ◽  
One Dimensional ◽  
Parameterization Method ◽  
Higher Dimensional

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

2022 ◽  
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Dynamic Characteristics ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Two Dimensional ◽  
Initial State ◽  
One Dimensional ◽  
Backward Euler ◽  
Short Period

Abstract The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

Chaos around Hyperbolic Fixed Points

1984 ◽  
Vol 53 (3) ◽  
pp. 895-898 ◽  
Author(s):  
Hajime Hirooka ◽  
Nobuhiko Saitô ◽  
Joseph Ford
Keyword(s):  
Fixed Points ◽  
Hyperbolic Fixed Points
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