TY - GEN
T1 - Hopf bifurcation in Hutchinson's equation with distributed delay
AU - Darti, I.
PY - 2014
Y1 - 2014
N2 - In this article we deal with the Hutchinson's equation with distributed delay dx(t)dt=rx(t)(1-a1x(t)-a2(t-τ)-a3 ∫ -∞tf(t-s)x(s) ds where r,τ,a1,a2,a3 are positive constants and f is the delay kernel function. By analyzing the associated characteristic equation, the local stability of positive equilibrium and Hopf bifurcation are investigated. The bifurcation here is controlled by the time delay. Some numerical simulations are performed to verify and illustrate the analytical findings.
AB - In this article we deal with the Hutchinson's equation with distributed delay dx(t)dt=rx(t)(1-a1x(t)-a2(t-τ)-a3 ∫ -∞tf(t-s)x(s) ds where r,τ,a1,a2,a3 are positive constants and f is the delay kernel function. By analyzing the associated characteristic equation, the local stability of positive equilibrium and Hopf bifurcation are investigated. The bifurcation here is controlled by the time delay. Some numerical simulations are performed to verify and illustrate the analytical findings.
KW - Distributed delay
KW - Hopf bifurcation
KW - Hutchinson's equation
UR - https://www.scopus.com/pages/publications/84904127564
U2 - 10.1063/1.4882471
DO - 10.1063/1.4882471
M3 - Conference contribution
AN - SCOPUS:84904127564
SN - 9780735412361
T3 - AIP Conference Proceedings
SP - 89
EP - 93
BT - Proceedings of the 3rd International Conference on Mathematical Sciences, ICMS 2013
PB - American Institute of Physics Inc.
T2 - 3rd International Conference on Mathematical Sciences, ICMS 2013
Y2 - 17 December 2013 through 19 December 2013
ER -