scholarly journals Positive Stability Analysis and Bio-Circuit Design for Nonlinear Biochemical Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yonghui Sun ◽  
Zhinong Wei ◽  
Guoqiang Sun
Keyword(s):  
Stability Analysis ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Positive Control ◽  
Biochemical Networks ◽  
Biochemical Network ◽  
Control Input ◽  
Convex Optimization Problem ◽  
Fuzzy Interpolation

This paper is concerned with positive stability analysis and bio-circuits design for nonlinear biochemical networks. A fuzzy interpolation approach is employed to approximate nonlinear biochemical networks. Based on the Lyapunov stability theory, sufficient conditions are developed to guarantee the equilibrium points of nonlinear biochemical networks to be positive and asymptotically stable. In addition, a constrained bio-circuits design with positive control input is also considered. It is shown that the conditions can be formulated as a solution to a convex optimization problem, which can be easily facilitated by using the Matlab LMI control toolbox. Finally, a real biochemical network model is provided to illustrate the effectiveness and validity of the obtained results.

Dynamical analysis of fractional-order differentiated Cournot triopoly game

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1367-1380
Author(s):  
Abdulrahman Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Periodic Forcing ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Theoretical Results

The objective of the article is to study the dynamics of the proposed fractional-order Cournot triopoly game. Sufficient conditions for the existence and uniqueness of the triopoly game solution are obtained. Stability analysis of equilibrium points of the fractional-order game is also discussed. The conditions for the presence of Nash equilibrium point along with its global stability analysis are studied. The interesting dynamical behaviors of the arbitrary-order Cournot triopoly game are discussed. Moreover, the effects of seasonal periodic forcing on the game’s behaviors are examined. The 0–1 test is used to distinguish between regular and irregular dynamics of system behaviors. Numerical analysis is used to verify the theoretical results that are obtained, and revealed that the nonautonomous fractional-order model induces more complicated dynamics in the Cournot triopoly game behavior and the seasonally forced game exhibits more complex dynamics than the unforced one.

Dynamical Study of Competition Cournot-like Duopoly Games Incorporating Fractional Order Derivatives and Seasonal Influences

2020 ◽  
Vol 21 (3-4) ◽  
pp. 339-359
Author(s):  
Abdulrahman Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Economic Systems ◽  
Cournot Duopoly ◽  
Dynamical Study ◽  
Nash Equilibrium Points ◽  
Time Varying Parameters ◽  
Memory Characteristics

AbstractCournot’s game is one of the most distinguished and influential economic models. However, the classical integer order derivatives utilized in Cournot’s game lack the efficiency to simulate the significant memory characteristics observed in many economic systems. This work aims at introducing a dynamical study of a more realistic proposed competition Cournot-like duopoly game having fractional order derivatives. Sufficient conditions for existence and uniqueness of the new model’s solution are obtained. The existence and local stability analysis of Nash equilibrium points along with other equilibrium points are examined. Some aspects of global stability analysis are treated. More significantly, the effects of seasonal periodic perturbations of parameters values are also explored. The multiscale fuzzy entropy measurements for complexity are employed for this case. Numerical simulations are presented in order to verify the analytical results. It is observed that the time-varying parameters induce very complicated dynamics in perturbed Cournot duopoly game compared with the unperturbed game.

Synchronization Stability Analysis of Medical Cyber-Physical Cloud System Considering Multi-Closed-Loops

2019 ◽  
Vol 28 (12) ◽  
pp. 1950198 ◽  
Author(s):  
Li Liu ◽  
Guoqi Xie ◽  
Renfa Li
Keyword(s):  
Cloud Computing ◽  
Stability Analysis ◽  
Lyapunov Stability ◽  
Physical System ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Dynamic Equations ◽  
Cloud System ◽  
Cyber Physical System ◽  
Closed Loops

Medical cyber-physical system (MCPS) is usually used in hospitals to provide continuous services (e.g., glycemic monitor and alarm) for patients. In this paper, we introduce cloud computing to integrate multiple MCPSs of hospitals to construct medical cyber-physical cloud system (MCPCS). Such complex MCPCS need stability analysis to guarantee collaboration among multiple MCPSs. We treat the MCPCS as a complex network, where each MCPS is considered as a node. Then, we introduce the Lyapunov stability theory for synchronization stability analysis of MCPCS by considering multi-closed-loops. For different network types, the dynamic equations of MCPSs were improved through introducing feedback in the multi-closed-loops. For the problem that different networks cause different delays, we select three networks to solve sufficient conditions for the synchronization stability of MCPCS. Experiments are performed to confirm the efficiency of sufficient conditions and the synchronization stability of MCPCS.

scholarly journals Stability Analysis of the Bat Algorithm Described as a Stochastic Discrete-Time State-Space System

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Janusz Piotr Paplinski
Keyword(s):  
Stability Analysis ◽  
State Space ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Bat Algorithm ◽  
Discrete Time System ◽  
Space System ◽  
State Matrix ◽  
State Space System

The main problem with the soft-computing algorithms is a determination of their parameters. The tuning rules are very general and need experiments during a trial and error method. The equations describing the bat algorithm have the form of difference equations, and the algorithm can be treated as a stochastic discrete-time system. The behaviour of this system depends on its dynamic and preservation stability conditions. The paper presents the stability analysis of the bat algorithm described as a stochastic discrete-time state-space system. The observability and controllability analyses were made in order to verify the correctness of the model describing the dynamic of BA. Sufficient conditions for stability are derived based on the Lyapunov stability theory. They indicate the recommended areas of the location of the parameters. The analysis of the position of eigenvalues of the state matrix shows how the different values of parameters affect the behaviour of the algorithm. They indicate the recommended area of the location of the parameters. Simulation results confirm the theory-based analysis.

scholarly journals Stability Analysis of Finance System Model with Information Effect

2020 ◽  
Vol 6 (1) ◽  
pp. 13-19
Author(s):  
Vivi Aida Fitria ◽  
Yudistira Arya Sapoetra
Keyword(s):  
Stability Analysis ◽  
Interest Rates ◽  
Equilibrium Points ◽  
Control Input ◽  
Point Of Interest ◽  
Investment Demand ◽  
Lack Of Information ◽  
Price Indexes ◽  
Analysis Of Stability ◽  
Analytical Result

Indonesia's participation in investing in the capital market is still very low, one of the causes is the lack of information. So this study discusses the analysis of stability in the financial system if influenced by information. We find that the model has two equilibrium point, that are point without interest rates and the price index of financial instruments and then the existing point of interest rates, the level of investment demand, price indexes and the influence of control input the information. The results of the local stability analysis of the equilibrium points are stable with certain conditions. The analytical result are confirmed by numerical simulations.

scholarly journals Complex dynamical behaviors of a novel exponential hyper–chaotic system and its application in fast synchronization and color image encryption

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042110033
Author(s):  
Javad Mostafaee ◽  
Saleh Mobayen ◽  
Behrouz Vaseghi ◽  
Mohammad Vahedi ◽  
Afef Fekih
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Sliding Mode ◽  
Color Image ◽  
Equilibrium Points ◽  
Lyapunov Stability Theory ◽  
System Stability ◽  
Color Image Encryption ◽  
Terminal Sliding Mode ◽  
Finite Time Stability

This paper proposes a novel exponential hyper–chaotic system with complex dynamic behaviors. It also analyzes the chaotic attractor, bifurcation diagram, equilibrium points, Poincare map, Kaplan–Yorke dimension, and Lyapunov exponent behaviors. A fast terminal sliding mode control scheme is then designed to ensure the fast synchronization and stability of the new exponential hyper–chaotic system. Stability analysis was performed using the Lyapunov stability theory. One of the main features of the proposed controller is the finite time stability of the terminal sliding surface designed with high–order power function of error and derivative of error. The approach was implemented for image cryptosystem. Color image encryption was carried out to confirm the performance of the new hyper–chaotic system. For image encryption, the DNA encryption-based RGB algorithm was used. Performance assessment of the proposed approach confirmed the ability of the proposed hyper–chaotic system to increase the security of image encryption.

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

scholarly journals Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Maoxing Liu ◽  
Jie Wu ◽  
Yong-zheng Sun
Keyword(s):  
Stability Analysis ◽  
Permanent Magnet ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Stability Control ◽  
Time Stability ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Comparison Results

We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

Stiffness of Cable-based Parallel Manipulators With Application to Stability Analysis

2005 ◽  
Vol 128 (1) ◽  
pp. 303-310 ◽  
Author(s):  
Saeed Behzadipour ◽  
Amir Khajepour
Keyword(s):  
Stability Analysis ◽  
Trajectory Planning ◽  
Stiffness Matrix ◽  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Rotational Stiffness ◽  
New Approach ◽  
Cable Forces

The stiffness of cable-based robots is studied in this paper. Since antagonistic forces are essential for the operation of cable-based manipulators, their effects on the stiffness should be considered in the design, control, and trajectory planning of these manipulators. This paper studies this issue and derives the conditions under which a cable-based manipulator may become unstable because of the antagonistic forces. For this purpose, a new approach is introduced to calculate the total stiffness matrix. This approach shows that, for a cable-based manipulator with all cables in tension, the root of instability is a rotational stiffness caused by the internal cable forces. A set of sufficient conditions are derived to ensure the manipulator is stabilizable meaning that it never becomes unstable upon increasing the antagonistic forces. Stabilizability of a planar cable-based manipulator is studied as an example to illustrate this approach.

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