References in periodicals archive ?
There are three singularities, two attractors, and one repeller (two stable equilibrium points and one unstable one), when m [greater than] 0.
The repeller is also a separatrix, which is the point that separates the two basins of attraction associated with the two attractors.
As we will discuss, structurally a saddle-node bifurcation can be thought of as a special case of the basin boundary collision, in that the repeller, which marks the boundary of the two basins, collides with the upper attractor, which is its own attractor boundary (since it is a single point).
By projecting from the peak of the function, for a given a value of r and solving for m such that projection intersects the lower repeller, it is easy to show that this point occurs when
3b, where it is obvious that the projection from the top of the map (which is the upper boundary of the strange attractor) intersects exactly at the repeller, which marks the position of the basin boundary.
The lower repeller generated complicated trajectories that appeared to be chaotic, but the potential boundaries of what had been a chaotic attractor intersected the basin boundaries of the upper point attractor, and thus those trajectories were formerly just part of the upper basin.
The market for nanoscale anti-microbial, easy-clean and self-cleaning coatings will grow across all sectors over the next few years, with the medical, household care and food processing markets all experiencing large growth, driven by the need for improved sanitary facilities and also pushed by the vast improvements these coatings offer as germ and dirt repellers.