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Proceeding of International Conference
Kazutoshi Kinoshita, Tetsushi Ueta, Bifurcation Analysis of the Lozi Map, as a Hybrid SystemProc. NOMA'09, 111-113, Urbino, Italy, Sep. 2009.
Abstract: We analyze bifurcations observed in the Lozi system. Since the state space is not differentiable at x = 0, the system becomes non invertible, and the solution and corresponding variations are not expressed by elementary functions, although the system is described by a piecewise linear equation. The system is classified as one of hybrid systems because of this non-smoothness. In spite of this factor, the orbit and variations can be differentiable at any moment except for x = 0, 1st and 2nd variations are obtained numerically, thus, in this paper, we compute bifurcations of the Lozi map by using a shooting method. We also report a special degenerated stable attractors keeping the Lyapunov stability criterion.

Contact address: ueta @