International Journal of Modern Nonlinear Theory and Application

Journal Information
ISSN / EISSN : 2167-9479 / 2167-9487
Published by: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 165
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Latest articles in this journal

Yerko Aguilera-Carvajal, Yonathan Tapia Robledo, Sebastián Perez Cortes
International Journal of Modern Nonlinear Theory and Application, Volume 10, pp 65-80; https://doi.org/10.4236/ijmnta.2021.102005

Abstract:
The current study is based on the DEM computer simulation of three experimental test devices with different dimensions to determine the difference in the results of the formation of shear and repose angles that the particles experience when grouped under the action of the gravitational force. In this respect, the experimental test devices with different height, width, and depth were geometrically modeled with iron pellet particles using morphology and a granulometric variation from 6 mm to 9 mm of equivalent diameter in its spherical shape. Depending on the results obtained, a reliable size of the experimental test device will be available to obtain the necessary data for a correct adjustment of the calibration parameters for the DEM simulation of mining-metallurgical processes that use granulated material of iron pellet.
Nurgul Bedelova, Avyt Asanov, Zhypar Orozmamatova, Zhypargul Abdullaeva
International Journal of Modern Nonlinear Theory and Application, Volume 10, pp 81-90; https://doi.org/10.4236/ijmnta.2021.102006

Abstract:
The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.
Ayman E. M. Ahmed, Mohamed Zohdy
International Journal of Modern Nonlinear Theory and Application, Volume 10, pp 1-12; https://doi.org/10.4236/ijmnta.2021.101001

Abstract:
In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction of the sliding mode controller for singularly perturbed systems. The controller design is based on a linear diagonal transformation of the singularly perturbed model. Furthermore, the use of a single sliding mode controller designed for the slow component of the diagonalized system is investigated. Simulation results indicate the performance improvement of the proposed controllers.
Suqi Ma
International Journal of Modern Nonlinear Theory and Application, Volume 10, pp 13-27; https://doi.org/10.4236/ijmnta.2021.101002

Abstract:
The observed dynamical property illustrates that state feedback control may stabilize invariant attractor to stable state in a simple version of hematopoietic stem cell model. The stability character of the positive steady state is analyzed by the computation of the rightmost characteristic roots in complex plane. Hopf bifurcation points are tracked as the roots curve crossing imaginary axis from the left half plane to the right half plane continuously. The bifurcation direction and stability of the bifurcating periodical solution are discussed by norm form computation combined with the center manifold theory. Furthermore, the numerical simulation verifies that instead of chaos, system is stabilized to period-1, 2, 3, 4 and period-7 periodical solutions in some delay windows, and the continuous of periodical solutions is also numerical simulated with varying free parameters continuously.
Suqi Ma Ma
International Journal of Modern Nonlinear Theory and Application, Volume 10, pp 91-105; https://doi.org/10.4236/ijmnta.2021.103007

Abstract:
The infinite dimensional partial delay differential equation is set forth and delay difference state feedback control is considered to describe the cell cycle growth in eukaryotic cell cycles. Hopf bifurcation occurs as varying free parameters and time delay continuously and the multi-layer oscillation phenomena of the homogeneous steady state of a simple gene-protein network module is investigated. Normal form is derived based on normal formal analysis technique combined with center manifold theory, which is further to compute the bifurcating direction and the stability of bifurcation periodical solutions underlying Hopf bifurcation. Finally, the numerical simulation oscillation phenomena is in coincidence with the theoretical analysis results.
S. Q. Ma
International Journal of Modern Nonlinear Theory and Application, Volume 10, pp 49-64; https://doi.org/10.4236/ijmnta.2021.102004

Abstract:
The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4+ T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4+ T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4+ T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.
S. Q. Ma
International Journal of Modern Nonlinear Theory and Application, Volume 10, pp 29-48; https://doi.org/10.4236/ijmnta.2021.102003

Abstract:
G0/G1 “gaps” joint the S phase and M phase to form the cell cycle. The dynamics of enzyme reaction to drive the target protein production in M phase is analyzed mathematically. Time delay is introduced since the signal transmission need time in G0/G1 “gaps” phase. Hopf bifurcation of DDEs model is analyzed by applying geometrical analytical method. The instability oscillating periodic solutions arise as subcritical Hopf bifurcation occurs. The Hysteresis phenomena of the limit cycle are also observed underlying the saddle-node bifurcation of the limit cycle. Due to stability switching, interestingly, the bifurcating periodical solution dies out near the vicinity of Hopf lines. By Lyapunov-Schmidt reduction scheme, the normal form is computed on the center manifold. Finally, it is verified that the theory analytical results are in coincidence with the numerical simulation.
Suqi Ma
International Journal of Modern Nonlinear Theory and Application, Volume 10, pp 106-118; https://doi.org/10.4236/ijmnta.2021.103008

Abstract:
A van der Pol equation underlying state feedback control is investigated and the triple-zero bifurcation arises at the bifurcation point which is of codimension three singularity. By applying Schmidt-Lyapunov reduction method combined with center manifold analytical technique, the near approximating formal norm is derived at the triple-zero point. Hence after, as varying parameters continuously, the numerical simulation produces homoclinic bifurcation solutions appearing in system. In addition, the numerical simulation also exhibits the produced double-period limit cycle with chosen bifurcation parameters and the routes to chaos via period-doubling bifurcation are also verified.
Messaoudi Khelifa
International Journal of Modern Nonlinear Theory and Application, Volume 09, pp 34-50; https://doi.org/10.4236/ijmnta.2020.92003

Abstract:
The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see [1] [2] [3]. We then consider a linear FS , and prove that, if ; , with the respective solutions of FS’s [A,B] and corresponding to the given (u,v) in . There exists,, positive real constants such that, . These results are the subject of theorems 3.1, ... , 3.3. The proofs of these theorems are based on our lemmas 3.2, ... , 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator I+BA and . The results obtained and demonstrated along this document, present an extension in general Banach space of those in [4] on a Hilbert space H and those in [5] on a extended Hilbert space .
Qiang Jiang, Dan Hu, Duyi He
International Journal of Modern Nonlinear Theory and Application, Volume 09, pp 1-18; https://doi.org/10.4236/ijmnta.2020.91001

Abstract:
The power grid is a fusion of technologies in energy systems, and how to adjust and control the output power of each generator to balance the load of the grid is a crucial issue. As a platform, the smart grid is for the convenience of the implementation of adaptive control generators using advanced technologies. In this paper, we are introducing a new approach, the Central Lower Configuration Table, which optimizes dispatch of the generating capacity in a smart grid power system. The dispatch strategy of each generator in the grid is presented in the configuration table, and the scenario consists of two-level agents. A central agent optimizes dispatch calculation to get the configuration table, and a lower agent controls generators according to the tasks of the central level and the work states during generation. The central level is major optimization and adjustment. We used machine learning to predict the power load and address the best optimize cost function to deal with a different control strategy. We designed the items of the cost function, such as operations, maintenances and the effects on the environment. Then, according to the total cost, we got a new second-rank-sort table. As a result, we can resolve generator’s task based on the table, which can also be updated on-line based on the environmental situation. The signs of the driving generator’s controller include active power and system’s f. The lower control level agent carries out the generator control to track f along with the best optimized cost function. Our approach makes optimized dispatch algorithm more convenient to realize, and the numerical simulation indicates the strategy of machine learning forecast of optimized power dispatch is effective.
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