Cyclic organization of stable periodic and chaotic pulsations in Hartley’s oscillator

2014 ◽  
Vol 59 ◽  
pp. 129-134 ◽  
Author(s):  
Joana G. Freire ◽  
Jason A.C. Gallas
Keyword(s):  
Stable Periodic ◽  
Cyclic Organization

scholarly journals Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Weibing Wang ◽  
Jianhua Shen ◽  
Juan J. Nieto
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Effect ◽  
Two Dimensional ◽  
Stable Periodic Solution ◽  
Predator Prey ◽  
Prey System ◽  
Stable Periodic ◽  
Holling Type Functional Response

We considered a nonautonomous two dimensional predator-prey system with impulsive effect. Conditions for the permanence of the system and for the existence of a unique stable periodic solution are obtained.

Open-loop stable running

Robotica ◽  
2005 ◽  
Vol 23 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Katja D. Mombaur ◽  
Richard W. Longman ◽  
Hans Georg Bock ◽  
Johannes P. Schlöder
Keyword(s):  
Optimization Methods ◽  
Open Loop ◽  
Bipedal Robots ◽  
Model Parameter ◽  
Stable Periodic ◽  
Parameter Values ◽  
Difficult Issue ◽  
Loop Stability

We present simulated monopedal and bipedal robots that are capable of open-loop stable periodic running motions without any feedback even though they have no statically stable standing positions. Running as opposed to walking involves flight phases which makes stability a particularly difficult issue. The concept of open-loop stability implies that the actuators receive purely periodic torque or force inputs that are never altered by any feedback in order to prevent the robot from falling. The design of these robots and the choice of model parameter values leading to stable motions is a difficult task that has been accomplished using newly developed stability optimization methods.

Hopf Bifurcation Induced by Delay Effect in a Diffusive Tumor-Immune System

2018 ◽  
Vol 28 (11) ◽  
pp. 1850136 ◽  
Author(s):  
Ben Niu ◽  
Yuxiao Guo ◽  
Yanfei Du
Keyword(s):  
Immune System ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Center Manifold ◽  
Immune Cell ◽  
Tumor Treatment ◽  
Delay Effect ◽  
Stable Periodic ◽  
The Stability ◽  
Bifurcation And Stability

Tumor-immune interaction plays an important role in the tumor treatment. We analyze the stability of steady states in a diffusive tumor-immune model with response and proliferation delay [Formula: see text] of immune system where the immune cell has a probability [Formula: see text] in killing tumor cells. We find increasing time delay [Formula: see text] destabilizes the positive steady state and induces Hopf bifurcations. The criticality of Hopf bifurcation is investigated by deriving normal forms on the center manifold, then the direction of bifurcation and stability of bifurcating periodic solutions are determined. Using a group of parameters to simulate the system, stable periodic solutions are found near the Hopf bifurcation. The effect of killing probability [Formula: see text] on Hopf bifurcation values is also discussed.

scholarly journals Modelling chronic hepatitis B using the Marchuk-Petrov model

2021 ◽  
Vol 2099 (1) ◽  
pp. 012036
Author(s):  
M Yu Khristichenko ◽  
Yu M Nechepurenko ◽  
D S Grebennikov ◽  
G A Bocharov
Keyword(s):  
Time Delay ◽  
Hepatitis B ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Stable Periodic ◽  
Delay Differential ◽  
Parameter Values

Abstract Systems of time-delay differential equations are widely used to study the dynamics of infectious diseases and immune responses. The Marchuk-Petrov model is one of them. Stable non-trivial steady states and stable periodic solutions to this model can be interpreted as chronic viral diseases. In this work we briefly describe our technology developed for computing steady and periodic solutions of time-delay systems and present and discuss the results of computing periodic solutions for the Marchuk-Petrov model with parameter values corresponding to the hepatitis B infection.

Sign in / Sign up

Export Citation Format

Share Document