Chaos and Bifurcation of Control Feedback System Using Variational Iteration Method
Evuiroro Edirin Judith,
Ojarikre Henritta Ify
Issue:
Volume 10, Issue 4, August 2021
Pages:
86-90
Received:
19 May 2021
Accepted:
15 June 2021
Published:
9 July 2021
Abstract: Chaos theory discusses the behavior of some complex systems which are sensitive to initial condition. It entails some interesting properties such as space-filling, sensitivity to initial conditions, control synchronization and dynamics which can be accessed using different control methods. This paper considers a non-linear feedback control system of underlying symmetries of chaos and bifurcation with periodic equations. Bifurcation theory plays a very vital role in the analysis of Chaos dynamics. Therefore, bifurcation process of chaotic systems involving Lyapunov exponents are studied. The work describes nonlinear systems where small changes produce notable change in the space phase with all the possible states corresponding to a unique point. A Variational Iteration Method (VIM) is adopted to determine the solution stability and bifurcation paths of the dynamic system. Thus. in the paper, state problems of the system are decomposed using Lagrange multiplier to obtain the Adomian polynomials. The polynomials generated in turn minimize the problem by providing an approximate solution that is very close to the analytic solution. A numerical illustration has been presented of a nonlinear coupled equation using VIM. Illustrations showing the graph of the phase space structure, the paths displayed in motion and the region of stability of the numerical scheme was obtained. The result shows that the chaotic nonlinear system is stable.
Abstract: Chaos theory discusses the behavior of some complex systems which are sensitive to initial condition. It entails some interesting properties such as space-filling, sensitivity to initial conditions, control synchronization and dynamics which can be accessed using different control methods. This paper considers a non-linear feedback control system o...
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The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission
Issue:
Volume 10, Issue 4, August 2021
Pages:
91-99
Received:
29 May 2021
Accepted:
21 June 2021
Published:
9 July 2021
Abstract: HIV spreads by cell-to-cell transfer and the release of cell-free particles. A slightly more effective method of retroviral transmission is the direct cell-to-cell transfer of HIV, according to recent reports. Intracellular interaction between unhealthy and healthy cells, in combination with cytokine discharged by the cells included, may affect the susceptibility of a target resting CD4+T cell to HIV infection and the formation of latent infection. We suggest a class of HIV latency mathematical model, integrating both cell-free virus transmission and direct cell-to-cell diffusion to improve the understanding of the dynamics of the latent reservoirs. We incorporate four components in our model: the uninfected T cells, the latently infected T cells, the active-infected T cells and the HIV viruses. We examine the latency model by introducing the basic reproduction number. We first establish the non-negativity and boundedness of the solutions of the system, and then we investigate the global stability of the steady states. The diseased-free equilibrium is globally stable when the basic reproduction number is less than 1 and if the basic reproduction number is greater than 1, the diseased equilibrium exists and is globally stable. Numerical simulations are executed to interpret the theoretical outcomes and evaluate the relative contribution of latency fractions in the virus production and the HIV latent reservoir by providing estimates.
Abstract: HIV spreads by cell-to-cell transfer and the release of cell-free particles. A slightly more effective method of retroviral transmission is the direct cell-to-cell transfer of HIV, according to recent reports. Intracellular interaction between unhealthy and healthy cells, in combination with cytokine discharged by the cells included, may affect the...
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