Anomalous diffusion, non-Gaussianity, nonergodicity, and confinement in stochastic-scaled Brownian motion with diffusing diffusivity dynamics

Brownian non-Gaussian polymer diffusion in non-static media

In nature, essentially, almost all the particles move irregularly in non-static media. With the advance of observation techniques, various kinds of new dynamical phenomena are detected, e.g., Brownian non-Gaussian diffusion. This paper focuses on the dynamical behavior of the center of mass (CM) of a polymer in non-static media and investigates the effect of polymer size fluctuations on the diffusion behavior. First, we establish a diffusing diffusivity model for polymer size fluctuations, linking the polymer size variation to the birth and death process, and introduce co-moving and physical coordinate systems to characterize the position of the CM for a polymer in non-static media. Next, the important statistical quantities for the CM diffusing diffusivity model in non-static media, such as mean square displacement (MSD) and kurtosis, are obtained by adopting the subordinate process approach, and the long-time asymptotic behavior of the MSD in the media of different types is specifically analyzed. Finally, the bivariate Fokker-Planck equation and the Feynman-Kac equation corresponding to the diffusing diffusivity model are detailedly derived and solved through the deep backward stochastic differential equation (BSDE) method to confirm the correctness of the derived equations.

Hamiltonian energy in a modified Hindmarsh-Rose model

This paper investigates the Hamiltonian energy of a modified Hindmarsh-Rose (HR) model to observe its effect on short-term memory. A Hamiltonian energy function and its variable function are given in the reduced system with a single node according to Helmholtz's theorem. We consider the role of the coupling strength and the links between neurons in the pattern formation to show that the coupling and cooperative neurons are necessary for generating the fire or a clear short-term memory when all the neurons are in sync. Then, we consider the effect of the degree and external stimulus from other neurons on the emergence and disappearance of short-term memory, which illustrates that generating short-term memory requires much energy, and the coupling strength could further reduce energy consumption. Finally, the dynamical mechanisms of the generation of short-term memory are concluded.