Abstract
•A hyperbolic system of two balance laws predicts instability and chaos.•Traveling-wave solutions undergo an Andronov–Hopf bifurcation and period-doubling bifurcations.•Simple modification of Fickett’s model captures most dynamics of one-dimensional detonations.
We present a computational analysis of a 2×2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in the model is varied. Linear and nonlinear stability properties of the traveling waves are computed numerically using accurate shock-fitting methods. The model may be considered as a minimal hyperbolic system with chaotic solutions and can also serve as a stringent numerical test problem for systems of hyperbolic balance laws.