Complex Dynamics of Economic Models with Time Delay

2020 ◽  
pp. 107-130
Author(s):  
Marek Szydłowski ◽  
Adam Krawiec
Keyword(s):  
Time Delay ◽  
Complex Dynamics ◽  
Economic Models

RICH DYNAMICS OF A TIME-DELAYED FOOD CHAIN MODEL

2006 ◽  
Vol 14 (03) ◽  
pp. 387-412 ◽  
Author(s):  
ALAKES MAITI ◽  
G. P. SAMANTA
Keyword(s):  
Computer Simulation ◽  
Time Delay ◽  
Functional Response ◽  
Food Chain ◽  
Complex Dynamics ◽  
Chain Model ◽  
Dynamical Behaviors ◽  
Discrete Time Delay ◽  
Food Chain Model ◽  
Practical Implications

Complex dynamics of a tritrophic food chain model is discussed in this paper. The model is composed of a logistic prey, a classical Lotka-Volterra functional response for prey-predator and a ratio-dependent functional response for predator-superpredator. Dynamical behaviors such as boundedness, stability and bifurcation of the model are studied critically. The effect of discrete time-delay on the model is investigated. Computer simulation of various solutions is presented to illustrate our mathematical findings. How these ideas illuminate some of the observed properties of real populations in the field is discussed and practical implications are explored.

Complex Dynamics of Landslides with Time Delay Under External Seismic Triggering Effect

2015 ◽  
pp. 1353-1356
Author(s):  
Srđan Kostić ◽  
Nebojša Vasović ◽  
Dragutin Jevremović ◽  
Duško Sunarić ◽  
Igor Franović ◽  
...  
Keyword(s):  
Time Delay ◽  
Complex Dynamics ◽  
Seismic Triggering

scholarly journals Global Robust Stabilization Control for Nonlinear Time-Delay Systems with Dead-Zone Input and Complex Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Lingrong Xue ◽  
Zhen-Guo Liu ◽  
Junjun Chen ◽  
Fujing Xu
Keyword(s):  
Time Delay ◽  
Control Method ◽  
Complex Dynamics ◽  
Dead Zone ◽  
Robust Stabilization ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Stabilization Control ◽  
Inequality Technique ◽  
Dynamic Subsystem

This article investigates the robust stabilization problem for nonlinear time-delay systems with dead-zone input and complex dynamics. By flexibly using the inequality technique, the backstepping control method, and skillfully introducing a new Lyapunov–Krasovskii functional, we obtain a stable controller without using unmeasurable signals in the dynamic subsystem. The control system is guaranteed to be stable finally. Two simulation examples are given to verify the control strategy.

scholarly journals Analysis of a Delayed SIR Model with Nonlinear Incidence Rate

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Jin-Zhu Zhang ◽  
Zhen Jin ◽  
Quan-Xing Liu ◽  
Zhi-Yu Zhang
Keyword(s):  
Time Delay ◽  
Incidence Rate ◽  
Incubation Time ◽  
Complex Dynamics ◽  
Threshold Value ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic ◽  
Saturated Form

An SIR epidemic model with incubation time and saturated incidence rate is formulated, where the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. The threshold valueℜ0determining whether the disease dies out is found. The results obtained show that the global dynamics are completely determined by the values of the threshold valueℜ0and time delay (i.e., incubation time length). Ifℜ0is less than one, the disease-free equilibrium is globally asymptotically stable and the disease always dies out, while if it exceeds one there will be an endemic. By using the time delay as a bifurcation parameter, the local stability for the endemic equilibrium is investigated, and the conditions with respect to the system to be absolutely stable and conditionally stable are derived. Numerical results demonstrate that the system with time delay exhibits rich complex dynamics, such as quasiperiodic and chaotic patterns.

Analysis on an Oscillator With Delayed Feedback Near Double Hopf Bifurcations

2001 ◽  
Author(s):  
P. Yu ◽  
Y. Yuan
Keyword(s):  
Time Delay ◽  
Nonlinear Oscillator ◽  
Analytical Approach ◽  
Complex Dynamics ◽  
Integration Scheme ◽  
Hopf Bifurcations ◽  
External Forcing ◽  
Chaotic Motions ◽  
System Parameters ◽  
Numerical Integration Scheme

Abstract This paper considers the effect of time delayed feedbacks in a nonlinear oscillator with external forcing. The particular attention is focused on the case where the corresponding linear system has two pairs of purely imaginary eigenvalues at a critical point, leading to double Hopf bifurcations. An analytical approach is used to find the explicit expressions for the critical values of the system parameters at which non-resonant or resonant Hopf bifurcations may occur. A fourth-order Ronge-Kutta numerical integration scheme is applied to obtain the dynamical solutions in the vicinity of the critical points. Both the cases with and without the external forcing are considered. It has been found the system exhibits very rich complex dynamics including periodic, quasi-periodic and chaotic motions. Moreover, a sensitivity analysis is carried out to show that chaotic motions are very sensitive to the time delay. This suggests that the time delay can be used: (1) to control bifurcations and chaos; and (2) to generate bifurcations and chaos.

Sequential Periodic Motions in a Vibration-Assisted, Regenerative, Nonlinear Turning-Tool System

2021 ◽  
Vol 31 (12) ◽  
pp. 2150186
Author(s):  
Siyuan Xing ◽  
Albert C. J. Luo
Keyword(s):  
Time Delay ◽  
Machine Tool ◽  
Complex Dynamics ◽  
Metal Removal ◽  
Removal Rate ◽  
Mapping Method ◽  
Strong Nonlinearity ◽  
Periodic Motions ◽  
Machine Vibration ◽  
Stability And Bifurcations

This paper studies the dynamics and bifurcations of a vibration-assisted, regenerative, nonlinear turning-tool system using an implicit mapping method. Machine vibration has been studied for a century for the improvement of machine accuracy and metal removal rate. In fact, this problem is unsolved yet. This is because such dynamical systems are involved in nonlinearity, discontinuity and time-delay. Thus, a comprehensive understanding of nonlinear machining dynamics with time-delay is indispensable. In this paper, period-[Formula: see text] motions in the turning machine-tool system are studied through specific mapping structures, and the corresponding stability and bifurcations of the period-[Formula: see text] motion are determined through the eigenvalue analysis. The analytical bifurcation scenarios for two sets of sequential period-[Formula: see text] motions in a turning-tool system are presented. Numerical simulations of period-[Formula: see text] motions are carried out to verify the prediction of periodic motions. The complex dynamics of vibration-assisted machining with strong nonlinearity are presented, which can provide a good overview for nonlinear dynamics of machine-tool systems.

A New Time-Delay Model for Chaotic Glucose-Insulin Regulatory System

2020 ◽  
Vol 30 (12) ◽  
pp. 2050178
Author(s):  
Abdul-Basset A. AL-Hussein ◽  
Fadhil Rahma ◽  
Luigi Fortuna ◽  
Maide Bucolo ◽  
Mattia Frasca ◽  
...  
Keyword(s):  
Time Delay ◽  
Complex Dynamics ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Regulatory System ◽  
Periodic Oscillation ◽  
Insulin Level ◽  
Insulin Degradation ◽  
Delay Model ◽  
New Time

Mathematical modeling is very helpful for noninvasive investigation of glucose-insulin interaction. In this paper, a new time-delay mathematical model is proposed for glucose-insulin endocrine metabolic regulatory feedback system incorporating the [Formula: see text]-cell dynamic and function for regulating and maintaining bloodstream insulin level. The model includes the insulin degradation due to glucose interaction. The dynamical behavior of the model is analyzed and two-dimensional bifurcation diagrams with respect to two essential parameters of the model are obtained. The results show that the time-delay in insulin secretion in response to blood glucose level, and the delay in glucose drop due to increased insulin concentration, can give rise to complex dynamics, such as periodic oscillation. These dynamics are consistent with the biological findings and period doubling cascade and chaotic state which represent metabolic disorder that may lead to diabetes mellitus.

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