Search

The research mentioned in the statement focuses on investigating a theoretical method for calculating the residence-times distribution function (RTDF) in a periodically driven, bistable system subject to noise recycling. This situation deviates from a Markovian process due to the recycling lag, making it challenging to determine the RTDF using traditional two-state models. In this paper, the aim is to overcome this issue and provide a systematic analysis of how to calculate the RTDF in such a system. By considering the piecewise escape rate of the system, which relies not only on the current state but also on the previous state, we have successfully derived the recursive expression of RTDF. Then, RTDF for large and small A/D is approximately derived using a piecewise analysis formula, respectively. It is further demonstrated both theoretically and numerically that the RTDF has exhibited a feedback-induced structure as a result of the recycling procedure. The results are shown as follows: for large A/D, the RTDF exhibits a series of sharp peaks located at odd multiples of approximately half the period of the driving signal. This indicates the occurrence of stochastic resonance. Additionally, it is interesting to note that the RTDF displays a sharp dip at t=τ. It is further shown that the process of noise recycling increases the probability of short residence times for t < τ and decreases the probability of long residence times for t>τ. This demonstrates that noise recycling plays a crucial role in facilitating particle hops between the double-well potential. For small A/D, the RTDF displays a phenomenon of piecewise exponential decay and declines sharply at t=τ. Notably, the interval between discontinuities becomes smaller or even disappears with increasing the noise intensity or the relative strength. Furthermore, when driven by an appropriate periodic signal, the RTDF exhibits a sequence of maximum values at odd multiples of approximately half the period of the driving signal. However, these maximum values disappear with increasing the noise intensity or the relative strength. This suggests that moderate noise recycling can induce the occurrence of stochastic resonance. However, excessive noise recycling actually inhibits the generation of stochastic resonance. The theoretical results have been successfully validated via numerical methods, demonstrating the reasonability of the present theoretical approach.

In light of the fact that existing centrality indexes disregard the influence of dynamic characteristics and lack generalizability due to standard diversification, this study investigates dynamic survivability centrality, which enables quantification of oscillators' capacity to impact the dynamic survivability of nonlinear oscillator systems. Taking an Erdős–Rényi random graph system consisting of Stuart–Landau oscillators as an illustrative example, the typical symmetry synchronization is considered as the key mission to be accomplished in light of the study and the dynamic survivability centrality value is found to be dependent on both the system size and connection density. Starting with a small scale system, the correctness of the theoretical results and the superiority in comparison to traditional indexes are verified. Further, we present the quantitative results by means of error analysis, distribution comparison of various indexes and relationship with system structure exploration, and give the position of the key oscillator. The results demonstrate a negligible error between the theoretical and numerical outcomes, and highlighting that the distribution of dynamic survivability centrality closely resembles the distribution of system state changes. The conclusions serve as evidence for the accuracy and validity of the proposed index. The findings provide an effective approach to protect systems to improve dynamic survivability. [ABSTRACT FROM AUTHOR]

The transient activity of the brain can be characterized by stable heteroclinic channels (SHCs) in the phase space of dynamical models, and the saddle points can represent the metastable states of brain activity. Inspired by this view, based on the hippocampal CA3–CA1 synaptic network model of memory we constructed earlier, we encode memory engrams as trajectories within the SHC in phase space. Short-term memory is transformed into long-term memory and then is encoded as trajectories within the SHC. The saddle points indicate the information blocks that have been segmented during the process of short-term memory. A stable heteroclinic network (SHN) is composed of multiple SHCs, whose trajectories express the memory engrams formed after the conversion of multiple short-term memories into long-term memories. From the existence conditions of SHC and SHN, the asymmetric regulation of neurotransmitters such as acetylcholine on the inhibition strength of adjacent postsynaptic neurons determines the capacity of short-term memory and participates in the encoding of long-term memory. Numerical results reveal the hysteresis effect of saddle points on the trajectories that reflect the limited capacity of short-term memory. All saddle points in the SHNs enable long-term memory to possess an extremely large capacity. Moreover, while noise in the hippocampal circuit can lead to the loss or confusion of memory information, it can also facilitate the encoding of long-term memories. The model and its theoretical analysis allow us to explain memory from the perspective of dynamics and have guiding significance for understanding the encoding and storage process of memory. [ABSTRACT FROM AUTHOR]

The spread of epidemic diseases is often considered to be bound up with human behavior. Both treatment and awareness-raising are seen as important preventive measures during an outbreak. In this paper, an SEIR model on heterogeneous network containing saturated treatment function with media information variable is constructed. Through mathematical analysis, the basic reproduction number and equilibriums of the system are derived. The global stability of disease-free equilibrium is further proved based on LaSalle's invariant principle. It is also found that with a gradual increase of the delayed treatment parameter, the system exhibits a transition from forward bifurcation to backward bifurcation with the variation of the basic reproduction number. Finally, an optimal control problem is formulated with both treatment rate and media information dissemination rate as control variables and solved using the Pontryagin's maximum principle. All the above results are verified by numerical experiments. [ABSTRACT FROM AUTHOR]