2021/03/13 by Alain M. Dikandé, Dikande, Alain M.
Materials Science · Physics and Astronomy · #Biological Physics (physics.bio-ph) #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Material Dynamics and Properties #Materials Science (cond-mat.mtrl-sci) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2103.07727
openalex publication_date 2021/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The texture of phase space and bifurcation diagrams of two-dimensional discrete maps describing a lattice of interacting oscillators, confined in on-site potentials with deformable double-well shapes, are examined. The two double-well potentials considered belong to a family proposed by Dikandé and Kofané (A. M. Dikandé and T. C. Kofané, Solid State Commun. vol. 89, p. 559, 1994), whose shapes can be tuned distinctively: one has a variable barrier height and the other has variable minima positions. However the two parametrized double-well potentials reduce to the ϕ4 substrate, familiar in the studies of structural phase transitions in centro-symmetric crystals or bistable processes in biophysics. It is shown that although the parametric maps are area preserving their routes to chaos display different characteristic features: the first map exhibits a cascade of period-doubling bifurcations with respect to the potential amplitude, but period-halving bifurcations with respect to the shape deformability parameter. On the other hand the first bifurcation of the second map always coincides with the first pitchfork bifurcation of the ϕ4 map. However, an increase of the deformability parameter shrinks the region between successive period-doubling bifurcations. The two opposite bifurcation cascades characterizing the first map, and the shrinkage of regions between successive bifurcation cascades which is characteristic of the second map, suggest a non-universal character of the Feigenbaum-number sequences associate with the two discrete parametric double-well maps.