Stochastic dynamic behavior of FitzHugh–Nagumo neurons stimulated by white noise

Stochastic noise exists widely in the nervous system, and noise plays an extremely important role in the information processing of the nervous system. Noise can enhance the ability of neurons to process information as well as decrease it. For the dynamic behavior of stochastic resonance and coherent resonance shown by neurons under the action of stochastic noise, this paper uses Fourier coefficient and coherence resonance coefficient to measure the behavior of stochastic resonance and coherence resonance, respectively, and some conclusions are drawn by analyzing the effects of additive noise and multiplicative noise. Appropriate noise can make the nonlinear system exhibit stochastic resonance behavior and enhance the detection ability of external signals. It can also make the coherent resonance behavior of the nonlinear system reach its optimal state, and the system becomes more orderly. By comparing the effects of additive and multiplicative noise on the stochastic resonance behavior and coherent resonance behavior of the system, it is found that additive and multiplicative noise can both make the system appear the phenomenon of stochastic resonance and have almost identical discharge state at the same noise intensity. However, with the increase of noise intensity, the coherent resonance of the system occurs, the multiplicative noise intensity is smaller than that of additive noise, but the coherent resonance coefficient of additive noise is smaller and the coherent resonance effect is better. The system whose system parameters are located near the bifurcation point is more prone to coherent resonance, and the closer the bifurcation point is, the more obvious the coherent resonance phenomenon is, and the more regular the system becomes. When the parameters of the system are far away from the bifurcation point, the coherent resonance will hardly appear. Besides, when additive and multiplicative noise interact together, the stochastic resonance and coherent resonance phenomena are more likely to appear at small noise, and the behavior of stochastic resonance and coherent resonance that the system shown is better in the local range.

Coherent energy transfer of a pair of two-level atoms

The coherent energy transfer efficiency of a pair of two-level atoms is studied theoretically and its mathematical expression has been deduced. The problem of atoms coherent energy transfer theory is treated by quantum perturbation theory and equivalent method replacing atomic dipole field with light field of the same frequency. The detuning between the donor atom transition frequency and the acceptor atom transition frequency has been studied in the theory. With the increase of the detuning of the two-atomic transition frequency, the energy transfer efficiency decays rapidly. In the case of two-atomic transition frequency resonance, the coherent resonance energy transfer efficiency is directly proportional to the square of the sine of the minus three power of the distance between two atoms and the energy transfer efficiency is periodically decaying over time. The coherent resonance energy transfer efficiency is inversely proportional to the six power of the distance between the two atoms in the first-order approximation.