Abstract
By using the method of symbolic dynamics, we study the bifurcations of steady states in a class of lattices of nonlinear discrete Klein–Gordon type with double-quadratic on-site potential. We derive by virtue of the admissible condition the critical value ε0 of the coupling strength, below which the steady states persist without bifurcations. If the coupling coefficient ε passes through the critical value, some of the steady states disappear. Meanwhile there are no new steady states created as ε varies. We obtain bifurcation values of some lower-order spatially periodic steady states by introducing the concept 'characteristic polynomial' of periodic sequences.
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