scholarly journals Flip and generalized flip bifurcations of a two-dimensional discrete-time chemical model

2021 ◽  
Vol 1 (2) ◽  
pp. 95-101
Author(s):  
Parvaiz Ahmad Naik ◽  
Zohreh Eskandari ◽  
Hossein Eskandari Shahraki
Keyword(s):  
Discrete Time ◽  
Chemical Model ◽  
Two Dimensional

scholarly journals Neimark–Sacker Bifurcation of a Two-Dimensional Discrete-Time Chemical Model

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
A. Q. Khan
Keyword(s):  
Lyapunov Exponent ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Oscillator Model ◽  
Chemical Model ◽  
Maximum Lyapunov Exponent ◽  
Two Dimensional ◽  
Unique Equilibrium ◽  
Bifurcation Diagrams ◽  
Local Dynamics

In this paper, the local dynamics and Neimark–Sacker bifurcation of a two-dimensional glycolytic oscillator model in the interior of ℝ+2 are explored. It is investigated that for all α and β, the model has a unique equilibrium point: Pxy+α/β+α2,α. Further about Pxy+α/β+α2,α, local dynamics and the existence of bifurcation are explored. It is investigated about Pxy+α/β+α2,α that the glycolytic oscillator model undergoes no bifurcation except the Neimark–Sacker bifurcation. Some simulations are given to verify the obtained results. Finally, bifurcation diagrams and the corresponding maximum Lyapunov exponent are presented for the glycolytic oscillator model.

Some ARMA models for dependent sequences of poisson counts

1988 ◽  
Vol 20 (4) ◽  
pp. 822-835 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Joint Distribution ◽  
Autoregressive Process ◽  
Two Dimensional ◽  
Arma Models ◽  
Time Reversibility ◽  
Vector Autoregressive ◽  
Arma Processes ◽  
Vector Autoregressive Process

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

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.

Degenerate Chenciner Bifurcation Revisited

2021 ◽  
Vol 31 (10) ◽  
pp. 2150160
Author(s):  
G. Tigan ◽  
O. Brandibur ◽  
E. A. Kokovics ◽  
L. F. Vesa
Keyword(s):  
Discrete Time ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Independent Parameters

Generic results for degenerate Chenciner (generalized Neimark–Sacker) bifurcation are obtained in the present work. The bifurcation arises from two-dimensional discrete-time systems with two independent parameters. We define in this work a new transformation of parameters, which enables the study of the bifurcation when degeneracy occurs. By the four bifurcation diagrams we obtained, new behaviors hidden by the degeneracy are brought to light.

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