scholarly journals On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Zhen Wang ◽  
Liwei Liu ◽  
Guangwang Su ◽  
Yuanfu Shao
Keyword(s):  
Time Delay ◽  
Food Web ◽  
Numerical Experiments ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Chaotic Oscillation ◽  
Mutual Interference ◽  
Web System ◽  
Distributed Time Delay ◽  
Theoretical Results

In this paper, we present a predator-prey system with mutual interference and distributed time delay and study its dynamical behavior. Based on the existence and universality of mutual interference among species, it is necessary to further study an impulsive food web system. By using stability theory, slight perturbation technique, and comparison theorem, we obtain some theoretical results of the system, such as boundedness and permanence. Moreover, numerical experiments are used to verify the theoretical results and to explore the dynamical behavior of the system, which exhibits rich dynamical behavior such as chaotic oscillation, periodic oscillation, symmetry-breaking bifurcations, chaotic crises, and period bifurcation. Finally, we give some practical guidelines for biological systems based on the theoretical results and numerical experiments of the system.

scholarly journals Analysis of mathematics and dynamics in a food web system with impulsive perturbations and distributed time delay

2010 ◽  
Vol 34 (12) ◽  
pp. 3850-3863 ◽  
Author(s):  
Xiaomei Wang ◽  
Hengguo Yu ◽  
Shouming Zhong ◽  
Ravi P. Agarwal
Keyword(s):  
Time Delay ◽  
Food Web ◽  
Web System ◽  
Distributed Time Delay ◽  
Impulsive Perturbations

Learning Control of Time-Delay Chaotic Systems and its Applications

1998 ◽  
Vol 08 (12) ◽  
pp. 2457-2465 ◽  
Author(s):  
Keiji Konishi ◽  
Hideki Kokame
Keyword(s):  
Control System ◽  
Time Delay ◽  
Chaotic System ◽  
Numerical Experiments ◽  
Chaotic Systems ◽  
Learning Control ◽  
Uncertain Information ◽  
Stable Orbit ◽  
One Dimensional ◽  
Theoretical Results

The present paper proposes a learning control system that automatically stabilizes one-dimensional time-delayed chaotic systems. We give a systematic procedure to design the control system using a few pieces of uncertain information on the chaotic system. Furthermore, this control system can be applied to a technique that moves a stable orbit of nonchaotic systems to coexistent unstable points and stabilizes the moving orbit onto these unstable points. To check the theoretical results, we demonstrate some numerical experiments.

scholarly journals The Vibration reduction of a cantilever beam subjected to parametric excitation using time delay feedback

2017 ◽  
Vol 13 (2) ◽  
pp. 7186-7193
Author(s):  
Y A Amer
Keyword(s):  
Time Delay ◽  
Cantilever Beam ◽  
Parametric Excitation ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Multiple Scale ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Resonance Case

In this paper, dynamical behavior of a cantilever beam subject to parametric excitation under state feedback control with time delay is analyzed. The method of multiple scale perturbation technique is applied to obtain the solution up to the first order approximation. We obtain equations for the amplitude and phase. We studied all resonance cases numerically. Stability of the steady state solution for the selected resonance case is studied applying Rung-Kutta fourth method and frequency response equation via Matlab 7.0 and maple 16. From the results, it can be seen that the frequency and amplitude responses for the selected resonance case can be affected by the time delayed control. Effects of different parameters of the system are studied.

Chaotic Dynamical Behavior of Coupled One-Dimensional Wave Equations

2021 ◽  
Vol 31 (06) ◽  
pp. 2150115
Author(s):  
Fei Wang ◽  
Junmin Wang ◽  
Zhaosheng Feng
Keyword(s):  
Numerical Simulations ◽  
Wave Equations ◽  
Dynamical Behavior ◽  
Chaotic Oscillation ◽  
Van Der Pol ◽  
Velocity Feedback ◽  
One Dimensional ◽  
Theoretical Results ◽  
Dimensional Wave

In this paper, we consider the chaotic oscillation of coupled one-dimensional wave equations. The symmetric nonlinearities of van der Pol type are proposed at the two boundary endpoints, which can cause the energy of the system to rise and fall within certain bounds. At the interconnected point of the wave equations, the energy is injected into the system through an anti-damping velocity feedback. We prove the existence of the snapback repeller when the parameters enter a certain regime, which causes the system to be chaotic. Numerical simulations are presented to illustrate our theoretical results.

scholarly journals Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liang’an Huo ◽  
Xiaomin Chen
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Functional Response ◽  
Response Function ◽  
Rapid Development ◽  
Dynamical Behavior ◽  
Deterministic System ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Holling Ii Functional Response

AbstractWith the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

scholarly journals Dynamical analysis of a giving up smoking model with time delay

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zizhen Zhang ◽  
Ruibin Wei ◽  
Wanjun Xia
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory

AbstractIn this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.

scholarly journals An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 994
Author(s):  
Elisa Alòs ◽  
Jorge A. León
Keyword(s):  
Malliavin Calculus ◽  
Numerical Experiments ◽  
Implied Volatility ◽  
Natural Approach ◽  
Volatility Models ◽  
Implied Volatility Surface ◽  
Short Memory ◽  
White Type ◽  
Volatility Surface ◽  
Theoretical Results

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

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