Related papers: Dynamic intersectoral models with power-law memory
Memory imprints of the significance of relationships are constantly evolving. They are boosted by social interactions among people involved in relationships, and decay between such events, causing the relationships to change. Despite the…
This work presents an analytical and computational study of fractional-order delay differential equations formulated using both the conformable and Caputo derivatives. For the conformable case, we develop the associated integral,…
Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems…
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…
Competitive dynamics are thought to occur in many processes of learning involving synaptic plasticity. Here we show, in a game theory-inspired model of synaptic interactions, that the competition between synapses in their weak and strong…
In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…
Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles,…
Memories in neural system are shaped through the interplay of neural and learning dynamics under external inputs. By introducing a simple local learning rule to a neural network, we found that the memory capacity is drastically increased by…
The power law has been observed in the degree distributions of many biological neural networks. Sparse deep neural networks, which learn an economical representation from the data, resemble biological neural networks in many ways. In this…
The Continuous Opinions and Discrete Actions (CODA) model has been widely used to study the emergence of extremism in social networks. However, this standard model has been shown to generate unrealistic extreme opinions due to the…
Recent advances in learning dynamical systems from data have shown significant promise. However, many existing methods assume access to the full state of the system -- an assumption that is rarely satisfied in practice, where systems are…
The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change…
We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modelled…
A mass of traces of human activities show diverse dynamic patterns. In this paper, we comprehensively investigate the dynamic pattern of human attention defined by the quantity of interests on subdisciplines in an online academic…
In this paper we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a…
We address memory effects in the dynamics of a two-level open quantum system interacting with a classical fluctuating field via dipole interaction. In particular, we study the backflow of information for a field with a Lorentzian spectrum,…
World models enable agents to plan within imagined environments by predicting future states conditioned on past observations and actions. However, their ability to plan over long horizons is limited by the effective memory span of the…
Properties of the phase space of the standard maps with memory obtained from the differential equations with the Riemann-Liouville and Caputo derivatives are considered. Properties of the attractors which these fractional dynamical systems…
A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…
The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and…