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This leads to a prediction that noise can induce multiple stable bumps, which we confirm numerically.
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For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches.
Logarithm of the probability of the bump width Δ when the local probability distribution is given by a shifted exponential and the covariance function is Gaussian: all bumps (top), stable bumps (middle), unstable bumps (bottom).
When (epsilon=0) bumps only exist below a critical value of (h_{0}), and a branch of stable bumps coalesces with a branch of unstable bumps at this critical value when (h_{0}) is varied.
The insets show the shapes of the lower (stable) bumps at (kappa= 0.7) for (q(x)) (blue) and (z(x)) (red).
In this investigation, system (2.3) has multiple stable equilibrium points.
Just as in default logic, some sets of assumptions have no stable extensions while some have multiple stable extensions.
Possible applications of composites with multiple stable geometries are noted.
The noble gases up to xenon have multiple stable isotopes.
Multiple stable clones were used to eliminate potential clonal effects.
Furthermore, multiple stable caveolae were detected in the cell periphery.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com