Physics Letters A 323 (2004) 67–76 www.elsevier.com/locate/pla Cosymmetric families of steady states in Darcy convection and their collision B. Karasözen a,∗ , V.G. Tsybulin b a Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey b Department of Mathematics and Mechanics, Rostov State University, 344090 Rostov on Don, Russia Received 26 August 2003; received in revised form 14 January 2004; accepted 15 January 2004 Communicated by C.R. Doering Abstract Natural planar convection of incompressible fluid in a porous medium, the Darcy model is studied. This problem belongs to the class of cosymmetric systems for whose an emergence of a continuous family of steady states (equilibria) is possible. We study the evolution of several families of steady states in the case of wide enclosure and analyze new effects of collision and reorganization of such families.  2004 Elsevier B.V. All rights reserved. PACS: 02.30.Jr; 02.70.Bf; 47.55.Mh Keywords: Darcy equation; Cosymmetry; Finite differences; Spectral methods; Families of equilibria 1. Introduction The cosymmetry in dynamical system [1] can be a reason for the onset of the continuous family of steady states (equilibria) with variable spectrum. The cosymmetric family of equilibria differs from symmetric case for which all members of a family have an identical spectrum [2]. Cosymmetry implies a number of new effects, for example, instability on the part of the family, the delay of limit cycle branching off from the continuous family [3,4] and * Corresponding author. E-mail addresses: bulent@metu.edu.tr (B. Karasözen), tsybulin@math.rsu.ru (V.G. Tsybulin). the appearance of a two-dimensional invariant torus off a family of equilibria [5]. Local bifurcations accompanying a monotonic loss of stability of an equilibrium belonging to the cosymmetric family were studied theoretically in [6]. The investigation of global effects and subsequent transitions are the current tasks that can be studied only numerically. One of the interesting problems with cosymmetric families is the convection of the incompressible fluid in a porous medium based on Darcy model [1,2,7]. In a number of recent works the intriguing transformations of the families of steady states and complicated convection was observed in this problem [8–14]. The numerical studies of partial differential equations were based on spectral [9], finite-difference [12,16] and combination of spectral and finite-difference [13,14] 0375-9601/$ – see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.01.053