Abstract
We consider discretized systems of hyperbolic balance laws. Decoupling of the flow, associated with a central difference scheme, can lead to binary oscillations — even and odd numbered grid points, separately, provide time-evolutions of two distinct, different, separate profiles. Investigating the stability of this decoupling phenomenon, we encounter Hopf-like bifurcations in the absence of parameters. With some computer-algebra assistance, we describe the qualitative behavior near these bifurcation points. In particular we observe distinct even/odd profiles which oscillate periodically in time and, for arbitrarily fine discretization, exhibit preferred, nonzero phase relationships between adjacent discretization points.
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