Time delay induced multistability and complex dynamics in an impulsive model of endocrine regulation

2014 ◽  
Author(s):  
Zhanybai T. Zhusubaliyev ◽  
Alexander N. Churilov ◽  
Alexander Medvedev
Keyword(s):  
Time Delay ◽  
Complex Dynamics ◽  
Endocrine Regulation ◽  
Impulsive Model

scholarly journals Finite-Dimensional Hybrid Observer for Delayed Impulsive Model of Testosterone Regulation

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Diana Yamalova ◽  
Alexander Churilov ◽  
Alexander Medvedev
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Linear Time ◽  
Blood Stream ◽  
Endocrine Gland ◽  
Endocrine Regulation ◽  
System A ◽  
Finite Dimensional ◽  
Continuous Models ◽  
Impulsive Model

The paper deals with the model-based estimation of hormone concentrations that are inaccessible for direct measurement in the blood stream. Previous research demonstrated that the dynamics of nonbasal endocrine regulation can be closely captured by linear continuous models with time delays under a pulse-modulated feedback. The presence of continuous time delays is inevitable in such a model due to transport phenomena and the time necessary for an endocrine gland to produce a certain hormone quantity. Yet, thanks to the finite-dimensional reducibility of the linear time-delay part of the system, a finite-dimensional model can be used to reconstruct both the continuous and discrete states of the hybrid time-delay plant. A hybrid observer exploiting this possibility is suggested and analyzed by means of a discrete impulse-to-impulse mapping.

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.

Asymptotic Stability for an Impulsive Model of Hematopoiesis with Time Delay

2012 ◽  
Vol 204-208 ◽  
pp. 4506-4512
Author(s):  
Rui Chen ◽  
Pei Jun Ju
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Function Method ◽  
Uniform Stability ◽  
Uniform Asymptotic Stability ◽  
Lyapunov Function Method ◽  
Impulsive Model

A model of hematopoiesis with time delay and impulses is studied. Based on the Lyapunov function method, uniform stability and uniform asymptotic stability of the equilibria is discussed.

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.

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