Bistability
In a conservative force field, bistability stems from the fact that the potential energy has two local minima, which are the stable equilibrium points.
By mathematical arguments, a local maximum, an unstable equilibrium point, must lie between the two minima.
At rest, a particle will be in one of the minimum equilibrium positions, because that corresponds to the state of lowest energy.
Bistability is widely used in digital electronics devices to store binary data.
It is the essential characteristic of the flip-flop, a circuit which is a fundamental building block of computers and some types of semiconductor memory.
Bistability can also arise in biochemical systems, where it creates digital, switch-like outputs from the constituent chemical concentrations and activities.
It is also involved in loss of cellular homeostasis associated with early events in cancer onset and in prion diseases as well as in the origin of new species (speciation).
[6] Bistability can be generated by a positive feedback loop with an ultrasensitive regulatory step.
Positive feedback loops, such as the simple X activates Y and Y activates X motif, essentially link output signals to their input signals and have been noted to be an important regulatory motif in cellular signal transduction because positive feedback loops can create switches with an all-or-nothing decision.
[7] Studies have shown that numerous biological systems, such as Xenopus oocyte maturation,[8] mammalian calcium signal transduction, and polarity in budding yeast, incorporate multiple positive feedback loops with different time scales (slow and fast).
[7] Having multiple linked positive feedback loops with different time scales ("dual-time switches") allows for (a) increased regulation: two switches that have independent changeable activation and deactivation times; and (b) noise filtering.
In several typical examples, the system has only one stable fixed point at low values of the parameter.
A saddle-node bifurcation gives rise to a pair of new fixed points emerging, one stable and the other unstable, at a critical value of the parameter.
[9] Bistability can be modified to be more robust and to tolerate significant changes in concentrations of reactants, while still maintaining its "switch-like" character.
Without this double feedback, the system would still be bistable, but would not be able to tolerate such a wide range of concentrations.
[10] Bistability has also been described in the embryonic development of Drosophila melanogaster (the fruit fly).
[14] A prime example of bistability in biological systems is that of Sonic hedgehog (Shh), a secreted signaling molecule, which plays a critical role in development.
Shh functions in diverse processes in development, including patterning limb bud tissue differentiation.
This signaling network illustrates the simultaneous positive and negative feedback loops whose exquisite sensitivity helps create a bistable switch.
[6] Bistable chemical systems have been studied extensively to analyze relaxation kinetics, non-equilibrium thermodynamics, stochastic resonance, as well as climate change.
[6] In bistable spatially extended systems the onset of local correlations and propagation of traveling waves have been analyzed.
In an ensemble average over the population, the result may simply look like a smooth transition, thus showing the value of single-cell resolution.
Here trajectories can shoot between two stable limit cycles, and thus show similar characteristics as normal bi-stability when measured inside a Poincare section.
Bistability as applied in the design of mechanical systems is more commonly said to be "over centre"—that is, work is done on the system to move it just past the peak, at which point the mechanism goes "over centre" to its secondary stable position.
Many ballpoint and rollerball retractable pens employ this type of bistable mechanism.
An even more common example of an over-center device is an ordinary electric wall switch.
These switches are often designed to snap firmly into the "on" or "off" position once the toggle handle has been moved a certain distance past the center-point.
