In this paper we study the Lyapunov stability and Hopf bifurcation in a biological system which models the biological control of parasites of orange plantations. c © 2007 Elsevier Ltd. All rights reserved.

Time-periodic vortex flows in an enclosed circular cylinder driven by the rotation of one endwall are investigated experimentally and numerically. This work is motivated partly by the linear stability analysis of Gelfgat et al. J. Fluid Mech. 438, 363 2001 , which showed the existence of an axisymmetric double Hopf bifurcation, and the purpose of the experiment is to see if the nonlinear dynami...

and Applied Analysis 3 transformed into the following nondimensional form: dx dt x 1 − x t − τ1 − xy a1 bx c1y , dy dt y [ δ − β t − τ2 x t − τ2 ] , 1.4 where a1 a/K, c1 cr/α, δ s/r, β sh/α are the non-dimensional parameters and they are positive. The main purpose of this paper is to consider the effect of multiple delays on system 1.4 . The local stability of the positive equilibrium and the e...

In this paper, we introduce an extended Sprott E system by a general quadratic control scheme with 3 arbitrary parameters for the new system. The resulting system can exhibit codimension-one Hopf bifurcations as parameters vary. The control strategy used can be applied to create degenerate Hopf bifurcations at desired locations with preferred stability. A complex chaotic attractor with only one...

In this paper, we focus on a spatial Holling-type IV predator-prey model which contains some important factors, such as diffusion, noise (random fluctuations) and external periodic forcing. By a brief stability and bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and derive the symbolic conditions for Hopf and Turing bifurcation in the spatial domain. Based on the stab...

Emily Stone Department of Mathematical Sciences, The University of Montana, Missoula, MT 59812 U.S.A. Abstract In this paper we present stability analysis of a nonlinear model for chatter vibration in a drilling operation. The results build our previous work [1, 2], where the model was developed and the nonlinear stability of the vibration modes as cutting width is varied was presented. Here we...

A mathematical model is proposed to study the role of distributed delay on plankton ecosystem in the presence of a toxic producing phytoplankton. The model includes three state variables, namely, nutrient concentration, phytoplankton biomass, and zooplankton biomass. The release of toxic substance by phytoplankton species reduces the growth of zooplankton and this plays an important role in pla...

We consider a pair of delay-coupled limit cycle oscillators. Regarding the arithmetical average of two delays as a parameter, we investigate the effect of time delays on its dynamics, show that there exist stability switches for time delays under certain conditions, which do not occur for the corresponding coupled system without time delays. We give detailed and specific conditions determining ...