Sharif Digital Repository

This paper is concerned with global analysis of a delay SVEIR epidemiological model in a population of varying size. By using Lyapunov stability method and LaSalle's invariance principle for delay systems, we prove that when there is no endemic equilibrium, the disease free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally stable  

We investigate singular stochastic delay differential equations (SDDEs) in view of their long-time behavior. Using Lyons's rough path theory, we show that SDDEs can be solved pathwise and induce a continuous stochastic flow on the space of (Gubinelli's) controlled paths. In the language of random dynamical systems, this result shows that SDDEs induce a continuous cocycle on random fibers, or, more precisely, on a measurable field of Banach spaces. We furthermore prove a multiplicative ergodic theorem (MET) on measurable fields of Banach spaces that applies under significantly weaker structural and measurability assumptions than preceding METs. Applying it to linear SDDEs shows that the... 

In this paper, for the first time, chaotic behavior of a classical moving-mirror Fabry-Perot cavity is obtained by finding numerical solution of a system of delay differential equations (previously obtained by a phenomenological approach (T. Carmon, M. C. Cross, K. J. Vahala, Phys. Rev. Lett. 98 (2007) 167203)). Fourier transform of the electromagnetic power for different values of pump power is calculated. By increasing the power, a period-doubling route to chaos is observed. Since the quality factor of the cavity has an important role in the chaotic behavior, variation of Lyapunov exponent and threshold power for the onset of chaos versus quality factor are investigated. A near linear... 

In this paper, the stability of delay differential equations (DDEs), describing self-excited vibrations in a micro-milling process, is investigated based on semi-discretization (SD) method. Due to the stubby geometry of micro-tools, the shear deformation and rotary inertia effects are considered for modeling the structure. The extended Hamilton's principle is used to derive a detailed dynamical model of the spinning micro-tool with the support of misalignment in which the gyroscopic effects cause coupling of equations. Considering the actual geometry of the micro-end mill, exact dynamic stiffness (DS) formulations are developed to investigate the tool's free vibration characteristics. The... 

Chatter suppression is an important topic in any type of machining process. In this paper, orthogonal cutting process is modeled as a single degree of freedom dynamic system. A nonlinear delay differential equation is presented that models flank wear of the tool. Uncertainties in cutting velocity, tool wear size and parameters of the dynamic model are included in the model of cutting process. The force provided by a piezo-actuator is taken as the control input of the system. A sliding mode control scheme is used and an effective control law is derived which suppresses the chatter vibration. Results for two distinct cases of a sharp tool and a worn tool are presented and compared which shows... 

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing the pitchfork bifurcation of non-trivial rest point. The asymptotic stability and possible Hopf bifurcations of the trivial rest point are studied by analyzing the corresponding characteristic equation. Homoclinic, fold, and pitchfork bifurcations of limit cycles are found. The delay-dependent stability... 

Chatter suppression in machining processes results in more material removal rate, high precision and surface quality. In this paper, a single degree of freedom model of orthogonal turning process is used to set up the delay differential equation of motion with considering the tool wear effect as a contact force between the workpiece and tool flank surfaces. Sinusoidal spindle speed variations with different frequencies around the mean speed are modulated to disturb the regenerative mechanism. The optimal amplitudes of the speed modulations are found based on a genetic algorithm such that the input energy to the turning process is minimized. Results of the stability analysis and the... 

High-quality, high-production-rate machining operations are significantly hindered by the regenerative chatter. Therefore, chatter suppression is of great significance; and active control is one of the best ways to curb it. In this paper, the orthogonal turning process is modeled as a single-degree-of-freedom system that includes the effect of tool wear; and described through a delay differential equation (DDE). Based on the model, stability lobes diagrams are obtained by the trial and error. The actuator force is the input for the control system and the tool vibration is the output. A classical PID controller is designed to improve the stability of the process and curb the self-excited... 

Chatter suppression is of great importance for achieving high precision and surface quality in machining processes. A single degree of freedom model of orthogonal turning process is used to set up the nonlinear delay differential equation of motion. Tool wear effect is considered as the contact force between the workpiece and tool flank surfaces. Uncertainties in parameters of dynamic model and machining conditions are included in the model. An adaptive control strategy is applied for chatter suppression in cutting process. The force provided by a piezoactuator is the control input of the system. Results of stability analysis and adaptive control for two distinct cases of sharp and worn... 

In this paper, a tunable vibration absorber set (TVAs) is designed to suppress regenerative chatter in milling process (as a semi-active controller). An extended dynamic model of the peripheral milling with closed form expressions for the nonlinear cutting forces is presented. The extension part of the cutting tool is modeled as an Euler-Bernoulli beam with in plane lateral vibrations (x-y directions). Tunable vibration absorbers in x-y directions are composed of mass, spring and dashpot elements. In the presence of regenerative chatter, coupled dynamics of the system (including the beam and x-y absorbers) is described through nonlinear delay differential equations. Using an optimal... 

Chatter suppression is of great importance for achieving high precision and surface quality in machining processes. A single degree of freedom model of orthogonal turning process is used to set up the nonlinear delay differential equation of motion. Tool wear effect is considered as the contact force between the workpiece and tool flank surfaces. Uncertainties in parameters of dynamic model and machining conditions are included in the model. An adaptive control strategy is applied for chatter suppression in cutting process. The force provided by a piezoactuator is the control input of the system. Results of stability analysis and adaptive control for two distinct cases of sharp and worn... 

Dynamic vibration absorbers are used to reduce the undesirable vibrations in many applications such as electrical transmission lines, helicopters, gas turbines, engines, bridges, etc. Tuneable vibration absorbers (TVA) are also used as semi-active controllers. In this paper, the application of a TVA for suppression of chatter vibrations in the boring manufacturing process is presented. The boring bar is modeled as a cantilever Euler-Bernoulli beam and the TVA is composed of mass, spring and dashpot elements. In addition, the effect of spring mass is considered in this analysis. After formulation of the problem, the optimum specifications of the absorber such as spring stiffness, absorber...