Dynamics terminology
Bistability is a dynamic term that refers to the phenomenon of two stable equilibrium states in a system, corresponding to two local minima of the potential energy curve, separated by a potential barrier. The system can switch states across potential barriers under the influence of external energy, and is commonly used in fields such as mechanical switches and biochemical regulation.
This phenomenon is used as a binary storage unit in digital circuits and is applied to devices such as Schmitt triggers; In biological systems, processes such as cell differentiation and apoptosis are regulated through positive feedback mechanisms. If the dorsal ventral axis of fly embryo development is formed [2-3]; In mechanical engineering, it is used to optimize vibration reduction devices, such as bistable nonlinear energy traps that improve isolation performance through potential well transitions [4-5]. Mathematically, it can be described by a differential equation model, such as $ dot {y}=y (r-y ^ 2) $, which exhibits a supercritical bifurcation. The conditions for generation include positive feedback, signal filtering, and growth inhibition regulation [1].
Since the development of nonlinear dynamics in the 20th century, the bistable theory has been extended to fields such as climate modeling and neuroscience. For example, symmetry breaking in brain networks can induce bistable manifolds, and changes in coupling parameters can lead to stable state separation [6-7]. The engineering field has deepened its understanding of the bistable energy storage mechanism through bifurcation analysis, chaos threshold calculation, and other methods, promoting applications such as vibration control and energy capture [8-10].
Basic definition
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In terms of potential energy, a bistable system has two local potential energy minima, with a local maximum between them. An example of a bistable mechanical device is the switch of a lamp, which is either "on" or "off" but does not stay between the two.
In a conservative force field, bistability is based on the fact that there are three equilibrium points for potential energy, two of which are extremely small and one is extremely large. Through mathematical discussions, it is known that the maximum value must be between two minimum values. A particle in the ground state is located at one of the two equilibrium points, as this corresponds to the minimum energy. The maximum value can be seen as a barrier between them.
If a system obtains enough activation energy to cross a barrier (compared to the Arrhenius formula in chemical examples), then it can transition from one minimum energy state to another. After reaching the limit, the system will enter another minimum energy state after a relaxation time.
Bistability is widely used in digital electronic devices to store binary data. A bistable device stores 1-bit binary data in the form of one state representing "0" and the other state representing "1". It is also applied to relaxation oscillators, multi harmonic oscillators, and Schmitt triggers. Visual bistability refers to the distribution of specific visual devices. According to the input, there are two stable resonant transmission states among these devices. Bistability can also occur in biochemical systems, producing digital, switchable outputs from sustained chemical concentrations and reactions. In these systems, bistability is usually associated with hysteresis phenomena
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