1,901 research outputs found
Stability of stochastic impulsive differential equations: integrating the cyber and the physical of stochastic systems
According to Newton's second law of motion, we humans describe a dynamical
system with a differential equation, which is naturally discretized into a
difference equation whenever a computer is used. The differential equation is
the physical model in human brains and the difference equation the cyber model
in computers for the dynamical system. The physical model refers to the
dynamical system itself (particularly, a human-designed system) in the physical
world and the cyber model symbolises it in the cyber counterpart. This paper
formulates a hybrid model with impulsive differential equations for the
dynamical system, which integrates its physical model in real world/human
brains and its cyber counterpart in computers. The presented results establish
a theoretic foundation for the scientific study of control and communication in
the animal/human and the machine (Norbert Wiener) in the era of rise of the
machines as well as a systems science for cyber-physical systems (CPS)
Exponential Stability of Impulsive Delay Differential Equations
The main objective of this paper is to further investigate the exponential stability of a class of impulsive delay differential equations. Several new criteria for the exponential stability are
analytically established based on Razumikhin techniques. Some sufficient conditions, under which a class of linear impulsive delay differential equations are exponentially stable, are also given. An Euler method is applied to this kind of equations and it is shown that the exponential stability is preserved by the numerical process
A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent
asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and
Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National
Research Council of Thailand and Khon Kaen University, Thailand (6200069)
A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent
asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and
Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National
Research Council of Thailand and Khon Kaen University, Thailand (6200069)
On the modulation instability analysis and deeper properties of the cubic nonlinear Schr¨odinger’s equation with repulsive δ-potential
This projected work applies the generalized exponential rational function method to extract the complex, trigonometric, hyperbolic, dark bright soliton solutions of the cubic nonlinear Schrödinger’s equation. Moreover, trigonometric, complex, strain conditions and dark-bright soliton wave distributions are also reported. Furthermore, the modulation instability analysis is also studied in detail. To better understand the dynamic behavior of some of the obtained solutions, several numerical simulations are presented in the paper. According to the obtained results, it is clear that the method has less limitations than other methods in determining the exact solutions of the equations. Despite the simplicity and ease of use of this method, it has a very powerful performance and is able to introduce a wide range of different types of solutions to such equations. The idea used in this paper is readily applicable to solving other partial differential equations in mathematical physics.Fundación Séneca (Spain), grant 20783/PI/18., and Ministry of Science, Innovation and Universities (Spain), grant PGC2018-097198-B- 100. Moreoer, this projected work was partially (not financial) supported by Harran University with the project HUBAP ID:20124
New Trends in Differential and Difference Equations and Applications
This is a reprint of articles from the Special Issue published online in the open-access journal Axioms (ISSN 2075-1680) from 2018 to 2019 (available at https://www.mdpi.com/journal/axioms/special issues/differential difference equations)
Stability Analysis of Analytical and Numerical Solutions to Nonlinear Delay Differential Equations with Variable Impulses
A stability theory of nonlinear impulsive delay differential equations (IDDEs) is established. Existing algorithm may not converge when the impulses are variable. A convergent numerical scheme is established for nonlinear delay differential equations with variable impulses. Some stability conditions of analytical and numerical solutions to IDDEs are given by the properties of delay differential equations without impulsive perturbations
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