in this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.in the first approach, the equilibrium point of the system is one of the centers of the related membership fu...

finding a suitable estimation of stability domain around stable equilibrium points is an important issue in the study of nonlinear dynamical systems. this paper intends to apply a set of analytical-numerical methods to estimate the region of attraction for autonomous nonlinear systems. in mechanical and structural engineering, autonomous systems could be found in large deformation problems or c...

This paper examines a model of multi-jurisdiction formation where individuals’ characteristics are uniformly distributed over a finite interval. Every jurisdiction locates a public facility and distributes its cost equally among the residents. We consider two notions of stability: Nash stability and its refinement local Nash stability, and examine the existence and characterization of stable pa...

This paper introduces a methodology for soil slope stability analysis based on optimization, limit equilibrium principles and method of slices. In this study, the slope stability analysis problem is transformed into a constrained nonlinear optimization problem. To solve that, a Self-Adaptive Genetic Algorithm (GA) is utilized. In this study, the slope stability safety factors are the objective ...

rock slope stability depends very much on the strength features of the rock and the geometrical and strength characteristics of the discontinuities (e.g., roughness, wall strength and persistence). since a rock mass is not a continuum, its behavior is dominated by such discontinuities as faults, joints and bedding planes. also, rock slope instability is a major hazard for human activities and o...

The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

An interaction form is an abstract model of interaction based on a description of power distribution among agents over alternatives. A solution known as the settlement set is defined at any preference profile. Necessary and sufficient conditions for stability, that is the existence of settlements, are established. A Stability Index that plays a role similar to that of the Nakamura Number is def...

An epidemic model with optimal control strategies was investigated for Hepatitus C Viral disease that can be transmitted through infected individuals. In this study, we used a deterministic compartmental model for assessing the effect of different optimal control strategies for controlling the spread of Hepatitus C disease in the community. Stability theory of differential equations is us...