We study the exponential stability of Euler-Bernoulli beam with interior time delays and boundary damping. At first, we prove the well-posedness of the system by the C0 semigroup theory. Next we study the exponential stability of the system by constructing appropriate Lyapunov functionals. We transform the exponential stability issue into the solvability of inequality equations. By analyzing the relationship between delays parameters α and damping parameters β, we describe (β,α)-region for which the system is exponentially stable. Furthermore, we obtain an estimation of the decay rate λ⁎.
This paper is concerned with the problem of delay-dependent stability of time-delay systems. Firstly, it introduces a new useful integral inequality which has been proved to be less conservative than the previous inequalities. Next, the inequality combines delay-decomposition approach with uncertain parameters applied to time-delay systems, based on the new Lyapunov-Krasovskii functionals and new stability criteria for system with time-delay have been derived and expressed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness and the less conservative feature of the proposed method compared with some recent results.
We present a new approach to find travelling wave solutions for the Korteweg-de Vries type equations, which allows extending the class of known soliton solutions. Also we propose method for studying the multisoliton solutions of the Korteweg-de Vries type equations.
This is a continuation part of our investigation in which the second order nonlinear rational difference equation xn+1=(α+βxn+γxn-1)/(A+Bxn+Cxn-1), n=0,1,2,…, where the parameters A≥0 and B, C, α, β, γ are positive real numbers and the initial conditions x-1, x0 are nonnegative real numbers such that A+Bx0+Cx-1>0, is considered. The first part handled the global asymptotic stability of the hyperbolic equilibrium solution of the equation. Our concentration in this part is on the global asymptotic stability of the nonhyperbolic equilibrium solution of the equation.
Our goal in this paper is to investigate the global asymptotic stability of the hyperbolic
equilibrium solution of the second order rational difference equation
xn+1=α+βxn+γxn-1/A+Bxn+Cxn-1, n=0,1,2,…, where the parameters A≥0 and B, C, α, β, γ are positive real numbers and the initial conditions x-1, x0 are nonnegative real numbers such that A+Bx0+Cx-1>0.
In particular, we solve Conjecture 5.201.1 proposed by Camouzis and Ladas in their book (2008) which appeared previously in Conjecture 11.4.2 in Kulenović and Ladas monograph (2002).
We investigate behavior of solutions of the following systems of rational difference equations: xn+1=yn-3k-1/(±1±yn-(3k-1)xn-(2k-1)yn-(k-1)),yn+1=xn-3k-1/(±1±xn-3k-1yn-2k-1xn-k-1), where k is a positive integer and the initial conditions are real numbers. We show that every solution is periodic with 6k period, considerably improving the results in the literature.
The aim of this paper is to analyze a classical duopoly model introduced by Puu in 1991 when lower bounds for productions are added to the model. In particular, we prove that the complexity of the modified model is smaller than or equal to the complexity of the seminal one by comparing their topological entropies. We also discuss whether the dynamical complexity of the new model is physically observable.
The goal of this paper is to study the boundedness, the persistence, and the asymptotic behavior of the positive solutions of the system of two difference equations of exponential form: xn+1=a+be-yn+ce-xn/d+hyn, yn+1=a+be-xn+ce-yn/d+hxn, where a, b, c, d, and h are positive constants and the initial values x0, y0 are positive real values. Also, we determine the rate of convergence of a solution that converges to the equilibrium E=(x-,y-) of this system.
A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method.
We consider an almost periodic discrete Schoener’s competition model with delays. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result.
The Exponential Stability Result of an Euler-Bernoulli Beam Equation with Interior Delays and Boundary Damping