Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling

نویسندگان

  • Sue Ann Campbell
  • Yuan Yuan
  • Sharene D Bungay
چکیده

We consider a ring of identical elements with time delayed, nearest-neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The bifurcation and stability of nontrivial asynchronous oscillations from the trivial solution are analysed using equivariant bifurcation theory and centre manifold construction. Mathematics Subject Classification: 34K17, 37G40, 92B20

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Patterns of oscillation in a Ring of Identical Cells with Delayed Coupling

We investigate the behaviour of a neural network model consisting of three neurons with delayed self and nearest-neighbour connections. We give analytical results on the existence, stability and bifurcation of nontrivial equilibria of the system. We show the existence of codimension two bifurcation points involving both standard and D3-equivariant, Hopf and pitchfork bifurcation points. We use ...

متن کامل

Equivariant Hopf Bifurcation in a Ring of Identical Cells with Delay

A kind of delay neural network with n elements is considered. By analyzing the distribution of the eigenvalues, a bifurcation set is given in an appropriate parameter space. Then by using the theory of equivariant Hopf bifurcations of ordinary differential equations due to Golubitsky et al. 1988 and delay differential equations due to Wu 1998 , and combining the normal form theory of functional...

متن کامل

HOPF BIFURCATION CONTROL WITH PD CONTROLLER

In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...

متن کامل

Coupled cells with internal symmetry: I. Wreath products

In this paper and its sequel we study arrays of coupled identical cells that possess a ‘global’ symmetry group G, and in which the cells possess their own ‘internal’ symmetry group L. We focus on general existence conditions for symmetry-breaking steady-state and Hopf bifurcations. The global and internal symmetries can combine in two quite different ways, depending on how the internal symmetri...

متن کامل

Delayed feedback control of three diffusively coupled Stuart-Landau oscillators: a case study in equivariant Hopf bifurcation.

The modest aim of this case study is the non-invasive and pattern-selective stabilization of discrete rotating waves ('ponies on a merry-go-round') in a triangle of diffusively coupled Stuart-Landau oscillators. We work in a setting of symmetry-breaking equivariant Hopf bifurcation. Stabilization is achieved by delayed feedback control of Pyragas type, adapted to the selected spatio-temporal sy...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005