scholarly journals Dynamic Analysis and Synchronization with Unidirectional Coupling Involving Energy of a HR Neuron Under Electric Field and Memristive Autapse

2021 ◽  
Author(s):  
Shuai Qiao ◽  
Chenghua Gao ◽  
Xinlei An ◽  
Xingyue He ◽  
Jingjing Wang
Keyword(s):  
Hopf Bifurcation ◽  
Electric Field ◽  
Dynamic Analysis ◽  
Global Bifurcation ◽  
Magnetic Coupling ◽  
Regulation Mechanism ◽  
Quiescent State ◽  
Synaptic Coupling ◽  
Neuron Models ◽  
Unidirectional Coupling

Abstract Reliable neuron models play an important role in identifying the electrical activities, global bifurcation patterns, and dynamic mechanisms of neurons in complex electromagnetic environments. Considering the memristive autapse involving magnetic coupling has voltage-controlled, nonlinear, and memory, a 5-D HR neuron model containing magnetic field and electric field variables is established. Detailedly, the existence and stability conditions of the equilibrium point are determined by theoretical analysis, and the complex time-varying stability, saddle-node bifurcation, and Hopf bifurcation behaviors of the model are verified by numerical calculation. Interestingly, the system has a bistable structure consisting of quiescent state and period-1 and period-2 bursting modes near the subcritical Hopf bifurcation. It is noteworthy that the memristive autapse has a complex regulation mechanism for the bistable region so that three kinds of bistable coexisting structures and counterintuitive dynamic phenomena can be induced by appropriately adjusting the memristive autapse. Accordingly, the mechanism of positive feedback memristive autapse decreases its firing frequency, while negative feedback memristive autapse promotes its excitability was revealed by the fast-slow dynamic analysis. Extensive numerical results display that the system generally possesses period-adding bifurcation modes and comb-shaped chaotic structures. Furthermore, it is found that the firing modes and multistability regions of the system can be accurately predicted by analyzing the global dynamic behaviors of Hamilton energy. Importantly, it is verified that the unidirectional coupling controller involving energy is far more efficient and consumes less energy than electrical synaptic coupling in achieving complete synchronization with mismatched parameters.

Electric field controllable magnetic coupling of localized spins mediated by itinerant electrons: a toy model

2017 ◽  
Vol 19 (38) ◽  
pp. 26098-26106 ◽  
Author(s):  
Andrew Palii ◽  
Sergey Aldoshin ◽  
Boris Tsukerblat ◽  
Juan Modesto Clemente-Juan ◽  
Alejandro Gaita-Ariño ◽  
...  
Keyword(s):  
Electric Field ◽  
Mixed Valence ◽  
Magnetic Coupling ◽  
Itinerant Electron ◽  
Itinerant Electrons

In this paper, we propose a toy model to describe the magnetic coupling between the localized spins mediated by the itinerant electron in partially delocalized mixed-valence (MV) systems.

scholarly journals Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds

2009 ◽  
Vol 14 (4) ◽  
pp. 435-461 ◽  
Author(s):  
P. D. Gupta ◽  
N. C. Majee ◽  
A. B. Roy
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Global Bifurcation ◽  
Distributed Delay ◽  
Degree Theory ◽  
Homotopy Invariance ◽  
Normal Form Theory ◽  
Form Theory ◽  
Bam Neural Network ◽  
Uniqueness Of Equilibrium

In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and central manifold theorem. Lastly global bifurcation aspect of such periodic solutions is studied. Some numerical simulations for justifying the theoretical analysis are also presented.

scholarly journals Summary of Application of Magnetic Coupling Resonance Technology in Power Inspection UAV

2018 ◽  
Vol 228 ◽  
pp. 02007
Author(s):  
Ji Jiang ◽  
Xuanyi Liu ◽  
Xiaoming Zha
Keyword(s):  
Electric Field ◽  
Unmanned Aerial Vehicle ◽  
Technology Development ◽  
Magnetic Coupling ◽  
Research Literature ◽  
Status Quo ◽  
Field Inspection ◽  
Manual Inspection ◽  
The Status ◽  
Aerial Vehicle

With the improvement of technology, technology began to gradually applied to every field, electric field inspection also began to gradually enable unmanned aerial vehicle (uav) inspection instead of manual inspection. Articles in the domestic and foreign research literature of unmanned aerial vehicle (uav) magnetic coupling resonance charging basis, this paper introduces the unmanned aerial vehicle (uav) magnetic coupling resonance charging technology development and application of the status quo, points out the problems in the current study of, offers a new way for the further research in this field.

Analysis on Hopf Bifurcation and Complexity of one Kind Financial System

2011 ◽  
Vol 48-49 ◽  
pp. 813-816 ◽  
Author(s):  
Qi Zhang ◽  
Jun Hai Ma
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Dynamic Analysis ◽  
Dynamic Systems ◽  
Financial System ◽  
The Relationship ◽  
At Home

From a mathematical model of one kind complicated financial system, we make a dynamic analysis on this kind of system on the basis of studies of scholars both at home and abroad. We find characteristics of various dynamic systems driven by different parameters, and study possible Hopf bifurcation as well as the relationship between Hopf bifurcation and the values of parameters. Besides, we make use of algorithm to analyze complexity of the system. The results of numerical simulation prove that the theory used in the thesis is correct. This study is regarded with good theoretical and practical value.

Multi-parameter Hopf-bifurcation in Hodgkin–Huxley model exposed to ELF external electric field

2005 ◽  
Vol 26 (4) ◽  
pp. 1221-1229 ◽  
Author(s):  
Wang Jiang ◽  
Che Yanqiu ◽  
Fei Xiangyang ◽  
Li Li
Keyword(s):  
Hopf Bifurcation ◽  
Electric Field ◽  
External Electric Field

Studying on the Synchronization of a Mechanical Centrifugal Flywheel Governor System

2008 ◽  
Vol 385-387 ◽  
pp. 309-312
Author(s):  
Yan Dong Chu ◽  
Jian Gang Zhang ◽  
Xian Feng Li ◽  
Ying Xiang Chang
Keyword(s):  
Hopf Bifurcation ◽  
Chaos Synchronization ◽  
System Parameter ◽  
External Disturbance ◽  
Global Bifurcation ◽  
Lyapunov Stability Theory ◽  
Chaotic Synchronization ◽  
Bifurcation And Chaos ◽  
Proper System ◽  
Dynamical Behaviors

In this paper, the dynamical behaviors of the centrifugal flywheel governor with external disturbance are discussed, and the system exhibits exceedingly complicated dynamic behaviors. The influence of system parameter on the chaotic system is discussed through Lyapunov-exponents spectrum and global bifurcation diagram, which accurately portray the partial dynamic behavior of the system. It is chaotic with proper system parameter, and we utilize Poincaré sections to study the Hopf bifurcation and chaos forming of the centrifugal flywheel governor system. Then, we utilize coupled-feedback control and adaptive control to realize the chaotic synchronization and obtain the conditions of chaos synchronization. Finally, we carry on the theory proof using the Lyapunov stability theory to the obtained conditions, the theoretical proof and number simulation shows the effectiveness of these methods.

Dynamic Analysis of an SIRS Model with Nonlinear Incidence Rate

2012 ◽  
Vol 155-156 ◽  
pp. 23-26
Author(s):  
Jun Hong Li ◽  
Ning Cui ◽  
Liang Cui ◽  
Cai Juan Li
Keyword(s):  
Hopf Bifurcation ◽  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Dulac Function ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Disease Free

In this paper, we study the global dynamics of an SIRS epidemic model with nonlinear inci- dence rate. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asy- mptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the an- alytical results.

scholarly journals Modeling the effect of activation of CD4$^+$ T cells on HIV dynamics

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Linghui Yu ◽  
Zhipeng Qiu ◽  
Ting Guo
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Antiretroviral Therapy ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Activation Parameters ◽  
Quiescent State ◽  
Activation Effect ◽  
Hiv Dynamics ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>HIV infects active uninfected CD4<inline-formula><tex-math id="M1">\begin{document}$ ^+ $\end{document}</tex-math></inline-formula> T cells, and the active CD4<inline-formula><tex-math id="M2">\begin{document}$ ^+ $\end{document}</tex-math></inline-formula> T cells are transformed from quiescent state in response to antigenic activation. Activation effect of the CD4<inline-formula><tex-math id="M3">\begin{document}$ ^+ $\end{document}</tex-math></inline-formula> T cells may play an important role in HIV infection. In this paper, we formulate a mathematical model to investigate the activation effect of CD4<inline-formula><tex-math id="M4">\begin{document}$ ^+ $\end{document}</tex-math></inline-formula> T cells on HIV dynamics. In the model, the uninfected CD4<inline-formula><tex-math id="M5">\begin{document}$ ^+ $\end{document}</tex-math></inline-formula> T cells are divided into two pools: quiescent and active, and the stimuli rate of quiescent cells by HIV is described by saturated form function. We derive the basic reproduction number <inline-formula><tex-math id="M6">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> and analyze the existence and the stability of equilibria. Numerical simulations confirm that the system may have backward bifurcation and Hopf bifurcation. The results imply that <inline-formula><tex-math id="M7">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> cannot completely determine the dynamics of the system and the system may have complex dynamics, which are quite different from the models without the activation effect of CD4<inline-formula><tex-math id="M8">\begin{document}$ ^+ $\end{document}</tex-math></inline-formula> T cells. Some numerical results are further presented to assess the activation parameters on HIV dynamics. The simulation results show that the changes of the activation parameters can cause the system periodic oscillation, and activation rate by HIV may induce the supercritical Hopf bifurcation and subcritical Hopf bifurcation. Finally, we proceed to investigate the effect of activation on steady-state viral loads during antiretroviral therapy. The results indicate that, viral load may exist and remain high level even if antiretroviral therapy is effective to reduce the basic reproduction number below 1.</p>

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