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Complete Synchronization of a Time-Fractional Reaction-Diffusion System with Lorenz Nonlinearities
Published in Hemen Dutta, Mathematical Methods in Engineering and Applied Sciences, 2020
Abir Abbad, Salem Abdelmalek, Samir Bendoukha
Although chaotic ODE systems are useful in many applications, they may not be the most suitable for modeling some physical phenomena such as fluid dynamics. It is well known that fluid does not always flow in concentric circles. In fact, if the ratio between inertial forces and viscous forces, known as Reynolds number, is sufficiently small, the fluid particles flow in a seemingly chaotic fashion. Hence, to properly model their flow, one needs to consider the spatial dimension. This argument was first put forward by Cross and Hohenberg in [13], where they examined the dynamics of the complex Ginzburg–Landau and Kuramoto–Sivashinsky equations. More studies followed such as [14–15].
Equations and Ongoing Projects
Published in Pedro Ponce Cruz, Arturo Molina Gutiérrez, Ricardo A. Ramírez-Mendoza, Efraín Méndez Flores, Alexandro Antonio Ortiz Espinoza, David Christopher Balderas Silva, ®, 2020
Pedro Ponce Cruz, Arturo Molina Gutiérrez, Ricardo A. Ramírez-Mendoza, Efraín Méndez Flores, Alexandro Antonio Ortiz Espinoza, David Christopher Balderas Silva
In the case of dynamic system simulations, equations that involve one or more derivatives of a dependent variable with respect to a single independent variable, are known as ordinary differential equation (ODE). Consequently, MATLAB®’s Simulink uses different kind of solvers in order to iteratively find solutions to the ODE, in different time lapses. Therefore, for this case study, ode4 (Runge-Kutta) is selected since it is a fixed-step solver that allows us to make a numerical method approximation [47].
Deterministic and fractional analysis of a newly developed dengue epidemic model
Published in Waves in Random and Complex Media, 2023
Rahat Zarin, Mohabat Khan, Amir Khan, Abdullahi Yusuf
The novelty of the paper is the addition of the convex incidence rate and the conversion of the system of ordinary differential equations model to a set of fractional differential equations models. Three methods: the RK4, the NSFD, and the Newton polynomial are employed for the numerical solution of the system of ordinary and Fractional differential equations. This is an important addition to the existing model [37] in the context of dengue infection. Comparative performance of the state-of-the-art RK4 method with nonstandard finite difference method for the dengue model is performed. Furthermore, both the ordinary and fractional models are considered for a variety of initial conditions. In the case of the ODE model, the simulation results often do not match with the real situation.
Finite-time active fuzzy sliding mode approach for deep surge control in nonlinear disturbed compressor system with uncertainty in charactrisitic curve
Published in Automatika, 2021
Xiuwei Fu, Li Fu, Hamid Malekizade
Despite the introduction of numerous innovative models for compression systems, the Greitzer model is the main choice for active surge control in centrifugal compressors due to its low order equations and simple construction. This model can prepare a qualitative explanation of the relevant phenomena, while its simplicity enables the physical interpretation of the model parameters and their influence on the overall dynamics. In addition, a set of ordinary differential equations (ODE) makes real-time computations applicable and implementable. The reader is referred to [39] for comprehensive information on compressor system models and their use in surge control design.