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Control of Bifurcation in Internet Model with Time-Delay
Mohammad Darvishi,
Haji Mohammad Mohammadinejad
Issue:
Volume 5, Issue 5, October 2016
Pages:
186-192
Received:
1 September 2016
Accepted:
13 September 2016
Published:
8 October 2016
Abstract: In this paper we study the Hopf bifurcation control problem of a Internet Model with Time-delay. The stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply Proportional - Derivative (PD) controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulation results and figures confirm that the control strategy is efficient in controlling the Hopf bifurcation.
Abstract: In this paper we study the Hopf bifurcation control problem of a Internet Model with Time-delay. The stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering th...
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The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms
Issue:
Volume 5, Issue 5, October 2016
Pages:
193-201
Received:
13 October 2016
Published:
13 October 2016
Abstract: In this paper, the author proposed and considered a reaction-diffusion equation with diffusion terms and stage structure. We discussed the stability of the positive equilibrium. By using the upper-lower solutions and monotone iteration technique, we obtained the zero steady state and the boundary equilibrium were linear unstable and the unique positive steady state was globally asymptotic stability. The traditional results are improved and this result applies to broader frameworks.
Abstract: In this paper, the author proposed and considered a reaction-diffusion equation with diffusion terms and stage structure. We discussed the stability of the positive equilibrium. By using the upper-lower solutions and monotone iteration technique, we obtained the zero steady state and the boundary equilibrium were linear unstable and the unique posi...
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Smarandachely Adjacent-Vertex-Distinguishing Proper Edge Chromatic Number of Cm∨Kn
Issue:
Volume 5, Issue 5, October 2016
Pages:
202-206
Received:
16 October 2016
Published:
17 October 2016
Abstract: According to different conditions, researchers have defined a great deal of coloring problems and the corresponding chromatic numbers. Such as, adjacent-vertex-distinguishing total chromatic number, adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper total chromatic number. And we focus on the smarandachely adjacent-vertex-distinguishing proper edge chromatic number in this paper, study the smarandachely adjacent-vertex-distinguishing proper edge chromatic number of joint graph Cm∨Kn.
Abstract: According to different conditions, researchers have defined a great deal of coloring problems and the corresponding chromatic numbers. Such as, adjacent-vertex-distinguishing total chromatic number, adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-a...
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Some Direct Estimates for Linear Combination of Linear Positive Convolution Operators
B. Kunwar,
V. K. Singh,
Anshul Srivastava
Issue:
Volume 5, Issue 5, October 2016
Pages:
207-212
Received:
30 July 2016
Accepted:
12 August 2016
Published:
18 October 2016
Abstract: In this paper we have estimated some direct results for the even positive convolution integrals on C_2π, Banach space of 2 π - periodic functions. Here, positive kernels are of finite oscillations of degree 2k. Technique of linear combination is used for improving order of approximation. Property of Central factorial numbers, inverse formulas, mixed algebraic –trigonometric formula is used throughout the paper.
Abstract: In this paper we have estimated some direct results for the even positive convolution integrals on C_2π, Banach space of 2 π - periodic functions. Here, positive kernels are of finite oscillations of degree 2k. Technique of linear combination is used for improving order of approximation. Property of Central factorial numbers, inverse formulas, m...
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Distributed Subgradient Algorithm for Multi-Agent Convex Optimization with Global Inequality and Equality Constraints
Li Xiao,
Junjie Bao,
Xi Shi
Issue:
Volume 5, Issue 5, October 2016
Pages:
213-229
Received:
7 August 2016
Accepted:
5 October 2016
Published:
27 October 2016
Abstract: In this paper, we present an improved subgradient algorithm for solving a general multi-agent convex optimization problem in a distributed way, where the agents are to jointly minimize a global objective function subject to a global inequality constraint, a global equality constraint and a global constraint set. The global objective function is a combination of local agent objective functions and the global constraint set is the intersection of each agent local constraint set. Our motivation comes from networking applications where dual and primal-dual subgradient methods have attracted much attention in the design of decentralized network protocols. Our main focus is on constrained problems where the local constraint sets are identical. Thus, we propose a distributed primal-dual subgradient algorithm, which is based on the description of the primal-dual optimal solutions as the saddle points of the penalty functions. We show that, the algorithm can be implemented over networks with changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically converge to optimal solution with optimal value of the optimization problem under the Slater’s condition.
Abstract: In this paper, we present an improved subgradient algorithm for solving a general multi-agent convex optimization problem in a distributed way, where the agents are to jointly minimize a global objective function subject to a global inequality constraint, a global equality constraint and a global constraint set. The global objective function is a c...
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