Dynamic characteristics of a subcritical bifurcation with inversion symmetry

A unified model for the dynamics of driven ribbon with strain and magnetic order parameters

“…Moreover, a sixth order polynomial is most appropriate for describing martensites. For the case of magnetostrictive metallic glass samples, such a form can be made consistent with the speculation by Vohra et al [22][23][24][25][26] that weak magnetic nonlinearity drives the strong elastic nonlinearity by including appropriate magnetoelastic coupling. Third, as for the choice of the magnetoelastic coupling term, we use a weighted sum of symmetry preserving and symmetry breaking terms of the individual free energies of the two order parameters (for reasons explained below).…”

“…In their most general form, these equations explain several experimental results on the strain dynamics of the magnetostrictive metallic glass ribbons reported almost two decades ago [22][23][24][25][26] . Detailed numerical studies of the model equations show that these equations reproduce the period doubling route to chaos as a function of h dc keeping h ac fixed and also the quasiperiodic route to chaos as a function of h ac for a fixed dc field.…”

“…Indeed rich dynamics has been realized in experiments on magnetostrictive metallic glass ribbon [22][23][24][25][26][27] , almost twenty years ago. In a series of papers, Vohra and his group reported a host of dynamical features in the study of strain bifurcations in magnetostrictive metallic glass ribbons subjected to the combined influence of sinusoidal (ac) and dc magnetic fields [22][23][24][25][26][27] .…”

“…Indeed rich dynamics has been realized in experiments on magnetostrictive metallic glass ribbon [22][23][24][25][26][27] , almost twenty years ago. In a series of papers, Vohra and his group reported a host of dynamical features in the study of strain bifurcations in magnetostrictive metallic glass ribbons subjected to the combined influence of sinusoidal (ac) and dc magnetic fields [22][23][24][25][26][27] . In particular, they reported the quasiperioidic (QP) route to chaos when the amplitude of the sinusoidal applied magnetic field h ac was increased in the presence of an additional dc magnetic field h dc , while they found the period doubling (PD) route to chaos when h dc was increased keeping the ac field fixed 22,23 .…”

“…Most of these investigations are near equilibrium studies except the one that exploits the nonlinear dependence of the Young's modulus on the magnetic field in the fieldannealed samples 28,32 where the PD and QP routes to chaos have been reported 28 . However, the authors emphasize that rich dynamics exhibited by the metallic glass samples (listed above) [22][23][24][25][26][27] are not due to the ∆E effect 22,23 as the samples used are unannealed ribbons where the ∆E effect is insignificant. Some of these features have been explained using appropriate normal forms 33 by appealing to the universal nature of bifurcation phenomenon.…”