We show that in the neighbourhood of relative equilibria and relative periodic solutions, coordinates can be chosen so that the equations of motion, in normal form, admit certain additional equivariance conditions up to arbitrarily high order. In particular, normal forms for relative periodic solutions effectively reduce to normal forms for relative equilibria, enabling the calculation of the d...

The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low speed fluid away from the wall, has been studied experimentally, theoretically, and computationally for more than 50 years because of its importance to the three-dimensional structure of turbulent boundary layers. We produce five new three-dimensional solutions of turbulent plane Couette flow,...

We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrödinger equations. In fibre optics these equations can be used to model single mode fibers with strong birefingence and two-mode optical fibers. Recently these equations appear as model, which describe pulse-pulse interaction in wavelength-division-multiplexed channels of optical fiber transmissi...

In this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. The system is firstly, transformed into an ordinary differential equation by wave transformation. The solution of ODE is obtained by the homotopy perturbation method. To show the periodic behavior of the solution, a modification based on the Laplace transforms and...

In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhins continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the co...

We study the solutions of a system of three coupled excitable cells with D3 symmetry. The system has two parameters, one controls the local dynamics of each cell and the other the strength of the coupling. We find and describe self-sustained collective oscillations. Periodic solutions appear in global bifurcations, typically after the collapse of fixed points heteroclinically connected. The sym...

By using the continuation theorem of coincidence degree theory, sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic Lotka Volterra equations and systems with distributed or statedependent delays. Our results substantially extend and improve existing results. 2001 Academic Press

We study the existence of periodic solutions of the non–autonomous periodic Lyness’ recurrence un+2 = (an +un+1)/un, where {an}n is a cycle with positive values a,b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5–periodic. We prove that for each pair (a, b) 6= (1, 1) there are infinitely many initial conditions giving ris...