Turkish Journal of Computer and Mathematics Education, Apr 10, 2021
In this paper, we will use the differential equations of the SIR model as a non-linear system, by... more In this paper, we will use the differential equations of the SIR model as a non-linear system, by using the Runge-Kutta numerical method to calculate simulated values for known epidemiological diseases related to the time series including the epidemic disease COVID-19, to obtain hypothetical results and compare them with the dailyreal statisticals of the disease for counties of the world and to know the behavior of this disease through mathematical applications, in terms of stability as well as chaos in many applied methods. The simulated data was obtained by using Matlab programms, and compared between real data and simulated datd were well compatible and with a degree of closeness. we took the data for Italy as an application. The results shows that this disease is unstable, dissipative and chaotic, and the Kcorr of it equal (0.9621), ,also the power spectrum system was used as an indicator to clarify the chaos of the disease, these proves that it is a spread,outbreaks,chaotic and epidemic disease .
European Journal of Pure and Applied Mathematics, Apr 30, 2023
The Conjugate Gradient Method is a numerical optimization technique that finds the optimal soluti... more The Conjugate Gradient Method is a numerical optimization technique that finds the optimal solution by focusing on the coefficient conjugate. This paper presents a new coefficients conjugate gradient method for removing impulse noise from images, which is based on a quadratic function and is proven to be globally convergent. Results show that it is an effective method for image restoration.
European Journal of Pure and Applied Mathematics, Apr 30, 2023
Stability analysis of heat transfer (by Conduction, Convection, and Radiation) has been found for... more Stability analysis of heat transfer (by Conduction, Convection, and Radiation) has been found for a model of flow between two horizontal plates, one of them is thermally insulated. The stability measure through the neutral curve for this model shows that an increase of the buoyancy represented by Gershoff number (Gr) leads to an increase in stability region, especially for the considerable value of Reynolds number R. The results indicated that the effects of buoyancy forces have significant contribution to the field profiles
In this paper a new Rabinovitch-Fabrikant (R-F) four dimensional (4D) continuous time dynamical s... more In this paper a new Rabinovitch-Fabrikant (R-F) four dimensional (4D) continuous time dynamical system was generated from three dimensional (3D) Rabinovitch-Fabrikant dynamical system using the state augmentation technique by adding new state variables u. The system employs thirteen terms includes five cross-product terms and one irreversible function. The dynamical behaviors of the system were investigated which include equilibrium points, stability analysis, wave form analysis, phase space analysis, multistability, Hopf-bifurcation, the Lyapunov exponent and Lyapunov dimension. The values of Lyapunov exponents are:L1 = 14.025946, L2 = 0.295151, L3 = −2.854401, L4 = −13.736833. and Lyapunov dimension is (3.83474), so the system is unstable and hyperchaotic with coexistence attractors. Chaos was handled in two ways: adaptive control and adaptive synchronization, it was found that the new system is stable and achieved good results.
Date of publication (dd/mm/yyyy): 05/04/2021 Abstract – In this paper, a three dimensional non li... more Date of publication (dd/mm/yyyy): 05/04/2021 Abstract – In this paper, a three dimensional non linear discrete-time dynamical system was introduced, the numerical solution was carried by Newton's Raphson method. The basic properties was investigated by mean of it's fixed points, bifurcation and numerical diagrams. Stability analysis measured by eigenvalues of the characteristic equation roots ‘Lyapunov function and Jury's test which all show that the system is unstable. Chaos diagnose was calculated by Lyapunov exponent and binary test, the maximum value of Lyapunov exponent is obtain as ( 3.8), Lyapunov dimension is obtain as ( 2.0872) and binary test (0-1) is obtain as (k = 0.9942 1), which all shows the system is highly chaotic. Finally, the system was controlled effectively by designed feedback and adaptive controllers, the results after controls were very good system trajectories are stable and regular.
Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021
In this paper, we will use the differential equations of the SIR model as a non-linear system, by... more In this paper, we will use the differential equations of the SIR model as a non-linear system, by using the Runge-Kutta numerical method to calculate simulated values for known epidemiological diseases related to the time series including the epidemic disease COVID-19, to obtain hypothetical results and compare them with the dailyreal statisticals of the disease for counties of the world and to know the behavior of this disease through mathematical applications, in terms of stability as well as chaos in many applied methods. The simulated data was obtained by using Matlab programms, and compared between real data and simulated datd were well compatible and with a degree of closeness. we took the data for Italy as an application. The results shows that this disease is unstable, dissipative and chaotic, and the Kcorr of it equal (0.9621), ,also the power spectrum system was used as an indicator to clarify the chaos of the disease, these proves that it is a spread,outbreaks,chaotic an...
AL-Rafidain Journal of Computer Sciences and Mathematics, 2004
An algorithm for unconstrained minimization is proposed which is invariant to a non-linear scalin... more An algorithm for unconstrained minimization is proposed which is invariant to a non-linear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic function. It is derived for inexact line searches and is designed for general use, it compares favorably numerical tests [over eight test functions and dimensionally up to (2-100
In this paper 2D discrete time dynamical system is presented. The fixed points were found. The st... more In this paper 2D discrete time dynamical system is presented. The fixed points were found. The stability of fixed points is measured by characteristic roots, jury criteria, Lyapunov function. All show that the system is unstable, and analyzing the dynamic behavior of the system finds bifurcation diagrams at the bifurcation parameter. Newton's Raphson numerical method was used the roots of the system with the minimum error. Then, chaoticity is measured by the phase space; maximum Lyapunov exponent is obtain as (max 2.394569 L =); Lyapunov dimension is obtain as (3.366413 L D =); binary test (0-1) is obtain as (k = 0.982). All show that the system is chaotic. Finally, the adaptive control was performed. Moreover, theoretical and graphical results of the system after control show the system is stable and Lyapunov exponent is obtained as: 1 0.390000 L = − , 2 0.500000 L = − , so the system is regular.
Periodicals of Engineering and Natural Sciences (PEN), 2021
This paper contains many directions such as Estuary, Solute, Concentration, and Diffusion. Includ... more This paper contains many directions such as Estuary, Solute, Concentration, and Diffusion. Including a sample tube under a steady pressure gradient, the partial differential equations, and the ordinary differential is following the solution. The result comes from the reality that a probability of a mote crossing out of the element of the cross-sectional area of the flow is independent of some position of the cross-sectional element. Thus, the solute spread over a distance proportional to t 1/2 .
Periodicals of Engineering and Natural Sciences (PEN), 2021
It is implicit for some time ago, that the radiative magneto hydrodynamic stands for an interacti... more It is implicit for some time ago, that the radiative magneto hydrodynamic stands for an interacting between a radiation field and magneto hydrodynamic (MHD) field that is concerned with interacted electrical conducting fluids and electromagnetic field. An accurate solution to the heat transfer equation is obtained by calculating the radiant heat emission in the boundary layer MHD because of the eccentric rotations of the pore disk and the fluid for long time. It is found that the asymptotic solution is present in both the cases of suction and blowing states, whereas no such solution exists for the blowing state in the absence of radiative emission of heat. The heat transfer rate at the disk has been determined and the condition is gotten for the heat to flow from the liquid to the disk.
This research deals with designing a new electronic circuit as an engineering application on a fo... more This research deals with designing a new electronic circuit as an engineering application on a four-dimensional chaotic system. The adopted chaotic dynamical system with a hidden attractor consists of two quadratic nonlinearities and parameters. The electronic circuit model is obtained by applying Kirchhoff's laws. The electronic circuit consists of seven resistors, four capacitors, four voltages and four operational amplifiers. The chaotic motions of the four-Dimensional system are investigated through Lyapunov exponents, Kaplan-Yorke dimension, phase portraits, and diagrams. Using MultiSIM12, the theoretical results were simulated and found to be well consistent with the results obtained from MATLAB.
In this paper, we used four feedback control method to suppress a modified hyperchaotic Pan syste... more In this paper, we used four feedback control method to suppress a modified hyperchaotic Pan system to unstable equilibrium, and we found that the critical value for each method based on the Routh-Hurwitz theorem, we study the relationship between this value and asymptotically stable, unstable and Hopf Bifurcation. Finally, we found that the least complexity and cost of method depended only on the system's constants of critical value and do not depended on the method itself. Theoretical analysis, numerical simulation, illustrative examples and comparison are given to demonstrate the effectiveness of the proposed controllers.
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