International Journal of Modern Nonlinear Theory and Application

Journal Information
ISSN / EISSN : 21679479 / 21679487
Current Publisher: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 154
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Latest articles in this journal

Qiang Jiang, Dan Hu, Duyi He
International Journal of Modern Nonlinear Theory and Application, Volume 9, pp 1-18; doi: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.
Messaoudi Khelifa
International Journal of Modern Nonlinear Theory and Application, Volume 9, pp 34-50; doi: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 .
Azizi Tahmineh, Tahmineh Azizi
International Journal of Modern Nonlinear Theory and Application, Volume 9, pp 19-33; doi:10.4236/ijmnta.2020.92002

Abstract:
In this paper, we examine a discrete-time Host-Parasitoid model which is a non-dimensionalized Nicholson and Bailey model. Phase portraits are drawn for different ranges of parameters and display the complicated dynamics of this system. We conduct the bifurcation analysis with respect to intrinsic growth rate r and searching efficiency a. Many forms of complex dynamics such as chaos, periodic windows are observed. Transition route to chaos dynamics is established via period-doubling bifurcations. Conditions of occurrence of the period-doubling, Neimark-Sacker and saddle-node bifurcations are analyzed for b≠a where a,b are searching efficiency. We study stable and unstable manifolds for different equilibrium points and coexistence of different attractors for this non-dimensionalize system. Without the parasitoid, the host population follows the dynamics of the Ricker model.
Mio Kobayashi, Tetsuya Yoshinaga
International Journal of Modern Nonlinear Theory and Application, Volume 8, pp 1-16; doi:10.4236/ijmnta.2019.81001

Abstract:
This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can generate various phenomena including asymmetric fixed and periodic points. The Gaussian associative memory can effectively recall one of the stored patterns, which were triggered by an input pattern by associating the asymmetric two-periodic points observed in the coupled system with the binary values of output patterns. To investigate the Gaussian associative memory model, we formed its reduced model and analyzed the bifurcation structure. Pseudo-patterns were observed for the proposed model along with other conventional associative memory models, and the obtained patterns were related to the high-order or quasi-periodic points and the chaotic trajectories. In this paper, the structure of the Gaussian associative memory and its reduced models are introduced as well as the results of the bifurcation analysis are presented. Furthermore, the output sequences obtained from simulation of the recalling process are presented. We discuss the mechanism and the characteristics of the Gaussian associative memory based on the results of the analysis and the simulations conducted.
Guoguang Lin, Changqing Zhu
International Journal of Modern Nonlinear Theory and Application, Volume 8, pp 41-52; doi:10.4236/ijmnta.2019.82003

Mohammad Sharif Ullah, Golam Mostafa, Nusrat Jahan, Abdul Hakim Khan
International Journal of Modern Nonlinear Theory and Application, Volume 8, pp 53-61; doi:10.4236/ijmnta.2019.83004

Abstract:
Bangladesh is a densely populated country than many other countries of the world. The population growth is termed as alarming, however, knowledge of growth in the years to come would be useful in planning for the development of the country. This article is based on the projection of future population growth of the country. The available actual population census data during 1991-2011 of Bangladesh was applied to the application of a non-linear, non-autonomous ordinary differential equation familiar as Verhulst logistic population model with the maximum environmental capability of Bangladesh. Bangladesh will reach its carrying capacity of 245.09 million population in the next 56 years i.e. the year 2067 and then it decreases as S-shaped curve. The article has provided a focus on the changing trends of the growth of the population of Bangladesh.
Mengwei Li, Yuanfu Shao, Yafei Yang
International Journal of Modern Nonlinear Theory and Application, Volume 8, pp 93-105; doi:10.4236/ijmnta.2019.84007

Abstract:
This paper is concerned with a stochastic predator-prey system with Beddington-DeAngelis functional response and time delay. Firstly, we show that this system has a unique positive solution as this is essential in any population dynamics model. Secondly, the validity of the stochastic system is guaranteed by stochastic ultimate boundedness of the analyzed solution. Finally, by constructing suitable Lyapunov functions, the asymptotic moment estimation of the solution was given. These properties of the solution can provide theoretical support for biological resource management.
Ömür Umut, Serpil Yaşar
International Journal of Modern Nonlinear Theory and Application, Volume 8, pp 17-39; doi:10.4236/ijmnta.2019.81002

Abstract:
We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Padé approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist.
Naser Waheeb Alnaser, Waheeb Essa Alnaser
International Journal of Modern Nonlinear Theory and Application, Volume 8, pp 72-91; doi:10.4236/ijmnta.2019.83006

Wenbing Wu
International Journal of Modern Nonlinear Theory and Application, Volume 8, pp 62-71; doi:10.4236/ijmnta.2019.83005

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