The Experts below are selected from a list of 9 Experts worldwide ranked by ideXlab platform
Aja Remigius Okeke - One of the best experts on this subject based on the ideXlab platform.
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On Application of Lyapunov and Yoshizawa’s Theorems on Stability, Asymptotic Stability, Boundaries and Periodicity of Solutions of Duffing’s Equation
Asian Journal of Applied Sciences, 2014Co-Authors: Eze Everestus Obinwanne, Aja Remigius OkekeAbstract:Stability is one of the properties of solutions of any differential systems. A dynamical system in a state of equilibrium is said to be stable. In other words, a system has to be in a stable state before it can be asymptotically stable which means that stability does not necessarily imply asymptotic stability but asymptotic stability implies stability. For a system to be stable depends on the form and the space for which the system is formulated. Results are available for boundedness and periodicity of solutions of second order non-linear ordinary differential Equation. However, the issue of stability, asymptotic stability, with boundedness and periodicity of solutions of Duffing’s Equation is rare in literature. In this paper, our objective is to investigate the stability, asymptotic stability, boundedness and periodicity of solutions of Duffings Equation. We employed the Lyapunov theorems with some peculiarities and some exploits on the first order equivalent systems of a scalar differential Equation to achieve asymptotic stability and hence stability of Duffings Equation and again using Yoshizawas theorem we proved boundedness and periodicity of solutions of a Duffings Equation. Furthermore, we use fixed point technique and integrated Equation as the mode to confirm apriori-bounds in achieving periodicity and boundedness of the solution. The results obtained showed the consequences of the cyclic relationship between different properties of solutions because the asymptotic stability converges uniformly to a point and limit of the supremum of the absolute value of the difference between the distances existed and are unique and it is this uniqueness that implies the existence of stability. The space where this existed is the space which confirmed continuous closed and bounded nature of the solution and hence the existence of optimal solution and opened the window for application of abstract implicit function theorem in Banach’sSpace to guarantee uniqueness and asymptotic stability, ultimate boundedness and periodicity of solutions of Duffings Equation. We concluded that the objectives for the paper were achieved based on our deductions.
Eze Everestus Obinwanne - One of the best experts on this subject based on the ideXlab platform.
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On Application of Lyapunov and Yoshizawa’s Theorems on Stability, Asymptotic Stability, Boundaries and Periodicity of Solutions of Duffing’s Equation
Asian Journal of Applied Sciences, 2014Co-Authors: Eze Everestus Obinwanne, Aja Remigius OkekeAbstract:Stability is one of the properties of solutions of any differential systems. A dynamical system in a state of equilibrium is said to be stable. In other words, a system has to be in a stable state before it can be asymptotically stable which means that stability does not necessarily imply asymptotic stability but asymptotic stability implies stability. For a system to be stable depends on the form and the space for which the system is formulated. Results are available for boundedness and periodicity of solutions of second order non-linear ordinary differential Equation. However, the issue of stability, asymptotic stability, with boundedness and periodicity of solutions of Duffing’s Equation is rare in literature. In this paper, our objective is to investigate the stability, asymptotic stability, boundedness and periodicity of solutions of Duffings Equation. We employed the Lyapunov theorems with some peculiarities and some exploits on the first order equivalent systems of a scalar differential Equation to achieve asymptotic stability and hence stability of Duffings Equation and again using Yoshizawas theorem we proved boundedness and periodicity of solutions of a Duffings Equation. Furthermore, we use fixed point technique and integrated Equation as the mode to confirm apriori-bounds in achieving periodicity and boundedness of the solution. The results obtained showed the consequences of the cyclic relationship between different properties of solutions because the asymptotic stability converges uniformly to a point and limit of the supremum of the absolute value of the difference between the distances existed and are unique and it is this uniqueness that implies the existence of stability. The space where this existed is the space which confirmed continuous closed and bounded nature of the solution and hence the existence of optimal solution and opened the window for application of abstract implicit function theorem in Banach’sSpace to guarantee uniqueness and asymptotic stability, ultimate boundedness and periodicity of solutions of Duffings Equation. We concluded that the objectives for the paper were achieved based on our deductions.
Currie Anthony - One of the best experts on this subject based on the ideXlab platform.
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Chaotic dynamics in flows and discrete maps
1Co-Authors: Currie AnthonyAbstract:This work attempts to utilise perturbation theory to derive discrete mappings which describe the dynamical behaviour of a continuous, and a discrete, chaotic system. The first three chapters introduce some background to the theory of chaotic behaviour In discrete and continuous systems. Chapter 4 considers the dynamical behaviour of Duffings Equation. Perturbation theory is applied to Hamiltonian solutions of the system, and a 1-D mapping is derived which models the bifurcation of the system to chaos. Chapter 5 introduces a 2-D chaotic difference map. The qualitative dynamics of the system are investigated and a form of perturbation theory is applied to a parameterised version of the map. The perturbative solutions are shown to exhibit dynamical behaviour very like the original system
Herrera-ruiz Gilberto - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear model for the instability detection in centerless grinding process
'Faculty of Mechanical Engineering', 2015Co-Authors: Robles-ocampo, Jose Billerman, Jauregui-correa, Juan Carlos, Krajnik Peter, Sevilla-camacho, Perla Yasmin, Herrera-ruiz GilbertoAbstract:In this work a novel nonlinear model for centerless grinding is presented. The model describes the dynamic behavior of the process. The model considers that the systems stiffness depends on the existence of lobes in the workpiece surface. Lobes geometry is treated as a polygonal shape and it is demonstrated that the system can be represented as a Duffings Equation. It is shown that there is a critical lobe number, where the systems present an unstable behaviorthe critical lobe number is identified through the geometric stability index. Instabilities in the centerless grinding process are analyzed with two methods: the phase diagram and the continuous wavelet transform. The presented results show that the dynamic behavior of the centerless grinding process can be represented with a cubic stiffness function that is obtained from the analysis of the surface topology
Robles-ocampo, Jose Billerman - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear model for the instability detection in centerless grinding process
'Faculty of Mechanical Engineering', 2015Co-Authors: Robles-ocampo, Jose Billerman, Jauregui-correa, Juan Carlos, Krajnik Peter, Sevilla-camacho, Perla Yasmin, Herrera-ruiz GilbertoAbstract:In this work a novel nonlinear model for centerless grinding is presented. The model describes the dynamic behavior of the process. The model considers that the systems stiffness depends on the existence of lobes in the workpiece surface. Lobes geometry is treated as a polygonal shape and it is demonstrated that the system can be represented as a Duffings Equation. It is shown that there is a critical lobe number, where the systems present an unstable behaviorthe critical lobe number is identified through the geometric stability index. Instabilities in the centerless grinding process are analyzed with two methods: the phase diagram and the continuous wavelet transform. The presented results show that the dynamic behavior of the centerless grinding process can be represented with a cubic stiffness function that is obtained from the analysis of the surface topology
