scholarly journals Bifurcation control of a minimal model of marine plankton interaction with multiple delays

2021 ◽  
Vol 16 ◽  
pp. 16
Author(s):  
Zhichao Jiang ◽  
Maoyan Jie
Keyword(s):  
Control Method ◽  
Feedback Gain ◽  
Multiple Delays ◽  
Toxic Substances ◽  
Oscillatory Nature ◽  
Bifurcation Phenomena ◽  
Feedback Control Method ◽  
Delay Feedback Control ◽  
Three Delays ◽  
Delayed Model

Plankton blooms and its control is an intriguing problem in ecology. To investigate the oscillatory nature of blooms, a two-dimensional model for plankton species is considered where one species is toxic phytoplankton and other is zooplankton. The delays required for the maturation time of zooplankton, the time for phytoplankton digestion and the time for phytoplankton cells to mature and release toxic substances are incorporated and the delayed model is analyzed for stability and bifurcation phenomena. It proves that periodic plankton blooms can occur when the delay (the sum of the above three delays) changes and crosses some threshold values. The phenomena described by this mechanism can be controlled through the toxin release rates of phytoplankton. Then, a delay feedback controller with the coefficient depending on delay is introduced to system. It concludes that the onset of the bifurcation can be delayed as negative feedback gain (the decay rate) decreases (increases). Some numerical examples are given to verify the effectiveness of the delay feedback control method and the existence of crossing curve. These results show that the oscillatory nature of blooms can be controlled by human behaviors.

Generalized Hybrid Dislocated Function Projective Synchronization of Chaotic Systems with Time Delay

2014 ◽  
Vol 574 ◽  
pp. 672-678 ◽  
Author(s):  
Rui Li ◽  
Guang Jun Zhang ◽  
Tao Zhu ◽  
Xu Jing Wang ◽  
Jun Dong
Keyword(s):  
Time Delay ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Feedback Gain ◽  
Uncertain Parameters ◽  
Function Projective Synchronization ◽  
Feedback Control Method

In order to improve the security of secure communication, a novel generalized hybrid dislocated function projective synchronization (GHDFPS) was proposed and GHDFPS of time delay chaotic systems with uncertain parameters were researched in this paper. Due to time delay, the chaotic system can produce multiple positive Lyapunov exponential; this characteristic can enhance security in secure communications noticeably. Based on Lyapunove stability theory and modified hybrid feedback control method, the modified hybrid feedback controller and the parameter updating laws were designed for the GHDFPS between the two time delay chaotic systems with uncertain parameters. The feedback gain can be adjusted automatically according to the synchronization error values. Under the controller, generalized hybrid dislocated function projective synchronization of the two chaotic systems is achieved, and the uncertain parameters of response systems are identified. The chaotic item is added in the function scale factor. The chaotic item in the function scaling factor makes function scaling factor more complex and unpredictable. So this can enhance the features of indeterminism in secure communication. The time delay feedback Lorenz system as an example; by numerical simulations the effectiveness of the proposed method is demonstrated.

scholarly journals Vertical Vibration Control of Cold Rolling Mill’s Rolls Based on Time-delay Feedback Control Method

2018 ◽  
Vol 153 ◽  
pp. 06005
Author(s):  
Dongxiao Hou
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Cold Rolling ◽  
Rolling Mill ◽  
Control Method ◽  
Primary Resonance ◽  
Vertical Vibration ◽  
Resonance Amplitude ◽  
Feedback Control Method ◽  
Delay Feedback Control

In this paper, a two degree of freedom nonlinear vertical vibration equation of the cold rolling mill with the dynamic rolling force was established, then the delay feedback control method was introduced into the equation to controlled the vertical vibration of the system. The amplitude-frequency equations of primary resonance of system was carried out by using the multi-scale method, and the resonance characteristics of different parameters of delay feedback control method were obtained by adopting the actual parameters of rolling mill. It is found that the size of the resonance amplitude value was effectively controlled and the resonance region and jumping phenomenon of the system were eliminated by selecting the appropriate time-delay parameters combination, which provides an effective theoretical reference for solving mill vibration problems.

Car-following model based delay feedback control method with the gyroidal road

2019 ◽  
Vol 30 (09) ◽  
pp. 1950073 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Feedback Control ◽  
Traffic Flow ◽  
Delay Time ◽  
Control Method ◽  
Gain Coefficient ◽  
Car Following ◽  
Controller Gain ◽  
Car Following Model ◽  
Feedback Control Method ◽  
Delay Feedback Control

Connected vehicles are expected to become commercially available by the next decade. In this work, we propose a delay feedback control method for car-following model on a gyroidal road. By using the Hurwitz criteria and the condition for transfer function in terms of [Formula: see text]-norm, the impact of controller gain coefficient and the delay time on the performance of traffic flow is investigated. Based on the bode curve, we verify that the designed delay feedback controller is effective in suppressing traffic congestion and reducing energy consumption. The enhanced traffic flow model is more sensitive to the controller gain coefficient and delay time at downhill situation compared to the uphill situation. The conclusion obtained from the simulation example is consistent with the theoretical analysis.

scholarly journals On a New Cournot Duopoly Game

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
H. N. Agiza ◽  
A. A. Elsadany ◽  
M. M. El-Dessoky
Keyword(s):  
Nash Equilibrium ◽  
Control Method ◽  
Chaotic Behavior ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Feedback Control Method ◽  
Delay Feedback Control ◽  
Stability And Bifurcations ◽  
Theoretical Results

This paper presents a new Cournot duopoly game. The main advantage of this game is that the outputs are nonnegative for all times. We investigate the complexity of the corresponding dynamical behaviors of the game such as stability and bifurcations. Computer simulations will be used to confirm our theoretical results. It is found that the chaotic behavior of the game has been stabilized on the Nash equilibrium point by using delay feedback control method.

scholarly journals Delay Feedback Control of the Lorenz-Like System

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Qin Chen ◽  
Jianguo Gao
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Control Method ◽  
Functional Differential Equations ◽  
Variable Parameter ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Feedback Control Method ◽  
Delay Feedback Control

We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems.

scholarly journals Bionic Control of Cheetah Bounding with a Segmented Spine

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Chunlei Wang ◽  
Shigang Wang
Keyword(s):  
Control Method ◽  
Dynamic Properties ◽  
Biological Properties ◽  
The Body ◽  
Body Balance ◽  
Feedback Control Method ◽  
Dimensional Parameters ◽  
Delay Feedback Control ◽  
The Stability ◽  
Bounding Gait

A cheetah model is built to mimic real cheetah and its mechanical and dimensional parameters are derived from the real cheetah. In particular, two joints in spine and four joints in a leg are used to realize the motion of segmented spine and segmented legs which are the key properties of the cheetah bounding. For actuating and stabilizing the bounding gait of cheetah, we present a bioinspired controller based on the state-machine. The controller mainly mimics the function of the cerebellum to plan the locomotion and keep the body balance. The haptic sensor and proprioception system are used to detect the trigger of the phase transition. Besides, the vestibular modulation could perceive the pitching angle of the trunk. At last, the cerebellum acts as the CPU to operate the information from the biological sensors. In addition, the calculated results are transmitted to the low-level controller to actuate and stabilize the cheetah bounding. Moreover, the delay feedback control method is employed to plan the motion of the leg joints to stabilize the pitching motion of trunk with the stability criterion. Finally, the cyclic cheetah bounding with biological properties is realized. Meanwhile, the stability and dynamic properties of the cheetah bounding gait are analyzed elaborately.

scholarly journals Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Fang Zhang ◽  
Yanyan He
Keyword(s):  
Control Method ◽  
Complexity Analysis ◽  
Dynamic Properties ◽  
Stable Region ◽  
Largest Lyapunov Exponent ◽  
Game Model ◽  
Oligopoly Model ◽  
Long Run ◽  
Feedback Control Method ◽  
Delay Feedback Control

We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players.

scholarly journals Analysis of Complex Dynamics in Different Bargaining Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Xiaogang Ma ◽  
Chunyu Bao ◽  
Lin Su
Keyword(s):  
Supply Chain ◽  
Collective Bargaining ◽  
Control Method ◽  
Complex Dynamics ◽  
Control Factor ◽  
Feedback Control Method ◽  
Delay Feedback Control ◽  
The Stability ◽  
Risk And Benefit ◽  
Bargaining Behavior

This paper focuses on the bargaining behavior of supply chain members and studies the stability of the bargaining system. There are two forms of bargaining in the process of negotiation. One is separate bargaining, and the other is that the automobile manufacturers form an alliance and bargain with the supplier collectively. We explore the influence of bargaining power and adjustment speed on the stability of the dynamic system and find that both of the factors need to be small to maintain the stability of the supply chain. After comparing the two forms of bargaining in terms of profits and stable regions, we find that the collective bargaining is a pattern with the existence of risk and benefit simultaneously. In order to control chaos in collective bargaining to lower the risk, we adopt the delay feedback control method. With the introduction of the control factor, the system tends to be stable finally.

CONTROLLING CHAOS IN OPTICAL FIBER USING TIME-DELAY FEEDBACK CONTROL METHOD

2016 ◽  
Vol 28 (3) ◽  
pp. 195-203
Author(s):  
K. Zourmba ◽  
A. A. Oumate ◽  
B. Gambo ◽  
J. Y. Effa ◽  
A. Mohamadou
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Optical Fiber ◽  
Control Method ◽  
Controlling Chaos ◽  
Feedback Control Method ◽  
Delay Feedback Control
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