Bifurcation Analysis of Fractional Order Single Cell with Delay

2015 ◽  
Vol 25 (02) ◽  
pp. 1550020 ◽  
Author(s):  
Vedat Çelik
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Single Cell ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Stability Criterion ◽  
Order Model ◽  
Bifurcation Points ◽  
Fractional Order Model

This paper presents the bifurcation analysis of fractional order model of delayed single cell which is proposed for delayed cellular neural networks with respect to the time delay τ. The bifurcation points, time delay τc, are determined by modified Mikhailov stability criterion for a range of fractional delayed cell order 0.3 ≤ q < 1. Numerical results obtained from Adams–Bashforth–Moulton method demonstrate that the supercritical Hopf bifurcation occurs in the system.

scholarly journals A fractional-order love dynamical model with time delay for synergic couple : Stability analysis and Hopf bifurcation

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
The Impact

We investigate the fractional order love dynamic model with time delay for synergic couples in this manuscript. The quantitative analysis of the model has been done where the asymptotic stability of the equilibrium points of the model have been analyzed. Under the impact of time delay, the Hopf bifurcation analysis of the model has been done. The stability analysis of the model has been studied with the reproduction number less than or greater than 1. By using Laplace transformation, the analysis of the model has been done. The analysis shows that the fractional order model with a time delay can sufficiently improve the components and invigorate the outcomes for either stable or unstable criteria. In this model, all unstable cases are converted to stable cases under neighbourhood points. For all parameters, the reproduction ranges have been described. Finally, to illustrate our derived results numerical simulations have been carried out by using MATLAB. Under the theoretical outcomes from parameter estimation, the love dynamical system is verified.

Comparison of two different types of fractional-order COVID-19 distributed time-delay models with real data application

2021 ◽  
pp. 2150219
Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xinjian Zhuo
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Distributed Delay ◽  
Real Data ◽  
Least Square ◽  
Order Model ◽  
The Real ◽  
Fractional Order Model ◽  
Different Types ◽  
Distributed Time Delay

The outbreak of COVID-19 has a great impact on the world. Considering that there are different infection delays among different populations, which can be expressed as distributed delay, and the distributed time-delay is rarely used in fractional-order model to simulate the real data, here we establish two different types of fractional order (Caputo and Caputo–Fabrizio) COVID-19 models with distributed time-delay. Parameters are estimated by the least-square method according to the report data of China and other 12 countries. The results of Caputo and Caputo–Fabrizio model with distributed time-delay and without delay, the integer-order model with distributed delay are compared. These show that the fractional-order model can be better in fitting the real data. Moreover, Caputo order is better in short-term time fitting, Caputo–Fabrizio order is better in long-term fitting and prediction. Finally, the influence of several parameters is simulated in Caputo order model, which further verifies the importance of taking strict quarantine measures and paying close attention to the incubation period population.

scholarly journals Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Liu ◽  
Wei Chen ◽  
Kaiyu Qin ◽  
Ping Li
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Network Topology ◽  
Proof Of Concept ◽  
State Variables ◽  
Double Integral ◽  
Order Model ◽  
Fractional Order Model ◽  
The Relationship ◽  
Double Integrator

This paper is devoted to the consensus problems for a fractional-order multiagent system (FOMAS) with double integral and time delay, the dynamics of which are double-integrator fractional-order model, where there are two state variables in each agent. The consensus problems are investigated for two types of the double-integrator FOMAS with time delay: the double-integrator FOMAS with time delay whose network topology is undirected topology and the double-integrator FOMAS with time delay whose network topology is directed topology with a spanning tree in this paper. Based on graph theory, Laplace transform, and frequency-domain theory of the fractional-order operator, two maximum tolerable delays are obtained to ensure that the two types of the double-integrator FOMAS with time delay can asymptotically reach consensus. Furthermore, it is proven that the results are also suitable for integer-order dynamical model. Finally, the relationship between the speed of convergence and time delay is revealed, and simulation results are presented as a proof of concept.

scholarly journals Bifurcation Analysis of a Fractional-Order Delayed Rolling Mill’s Main Drive Electromechanical Coupling System

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rui Zhang ◽  
Jinbin Wang ◽  
Lifeng Ma
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Electromechanical Coupling ◽  
System Stability ◽  
Coupling System

This work is focused on a rolling mill’s main drive electromechanical coupling system. Firstly, we equip electromechanical coupling system with fractional-order time delay. Secondly, we, respectively, derive the conditions for occurrence of Hopf bifurcation around equilibriums E 0 0 , 0 , 0 , 0 and E 1 x 1 ∗ , 0 , x 3 ∗ , 0 . It is found that the fractional order α and time delay τ in the system play an important role on the system stability. Finally, numerical simulations are given to verify the analytic results.

scholarly journals Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Neural Networks With Time-Delay

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 158798-158807 ◽  
Author(s):  
Xiaohong Wang ◽  
Zhen Wang ◽  
Xianggeng Zhu ◽  
Bo Meng ◽  
Jianwei Xia
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Order Complex ◽  
Complex Valued

scholarly journals Stability and Hopf bifurcation analysis of fractional order nonlinear financial system with time delay

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Laplace Transformation ◽  
Financial System ◽  
System With Time Delay

In this paper, we study a fractional order time delay for nonlinear financial system. By using Laplace transformation, stability and Hopf bifurcation analysis have been done for the model. Furthermore, numerical simulation has been carried out for better understanding of our results.

scholarly journals Stability and Hopf Bifurcation Analysis of a Fractional-Order Epidemic Model with Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhen Wang ◽  
Xinhe Wang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Bifurcation Parameter ◽  
Theoretical Results ◽  
Disease Free

A fractional-order epidemic model with time delay is considered. Firstly, stability of the disease-free equilibrium point and endemic equilibrium point is studied. Then, by choosing the time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of theoretical results.

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