483 citations
- University of AucklandNZ53 papers
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8 papers · 1 filter
Chimeras with uniformly distributed heterogeneity: two coupled populations
Carlo R. Laing
Chimeras occur in networks of two coupled populations of oscillators when the oscillators in one population synchronise while those in the other are asynchronous. We consider chime…
Chaotic attractors from border-collision bifurcations: stable border fixed points and determinant-based Lyapunov exponent bounds
D. J. W. Simpson
The collision of a fixed point with a switching manifold (or border) in a piecewise-smooth map can create many different types of invariant sets. This paper explores two techniques…
Grazing-sliding bifurcations creating infinitely many attractors
David J. W. Simpson
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under…
The structure of mode-locking regions of piecewise-linear continuous maps: II. Skew sawtooth maps
David J. W. Simpson
In two-parameter bifurcation diagrams of piecewise-linear continuous maps on , mode-locking regions typically have points of zero width known as shrinking points. Nea…
The stability of fixed points on switching manifolds of piecewise-smooth continuous maps
David J. W. Simpson
This paper concerns piecewise-smooth maps on that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The st…
Stochastic Perturbations of Periodic Orbits with Sliding
David J. W. Simpson, Rachel Kuske
Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a di…