scholarly journals The rate of decay of stable periodic solutions for Duffing equation with L p -conditions

Author(s):  
Shuqing Liang
2018 ◽  
Vol 28 (11) ◽  
pp. 1850136 ◽  
Author(s):  
Ben Niu ◽  
Yuxiao Guo ◽  
Yanfei Du

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.


2021 ◽  
Vol 2099 (1) ◽  
pp. 012036
Author(s):  
M Yu Khristichenko ◽  
Yu M Nechepurenko ◽  
D S Grebennikov ◽  
G A Bocharov

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