Related papers: Dynamical Theory for Adaptive Systems
We introduce a novel, model-independent method for the efficient simulation of low-entropy systems, whose dynamics can be accurately described with a limited number of states. Our method leverages the time-dependent variational principle to…
A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…
Dynamical System has been widely used for encoding trajectories from human demonstration, which has the inherent adaptability to dynamically changing environments and robustness to perturbations. In this paper we propose a framework to…
Intraspecific trait variation has been increasingly recognized as an important factor in determining species interaction and diversity. Eco-evolutionary models have studied the distribution of trait values within a population that changes…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
We apply methods of dynamical systems to study the behaviour of the Randall-Sundrum models. We determine evolutionary paths for all possible initial conditions in a 2-dimensional phase space and we investigate the set of accelerated models.…
Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem based on importance sampling, cloning, and spectral…
Deep neural networks give us a powerful method to model the training dataset's relationship between input and output. We can regard that as a complex adaptive system consisting of many artificial neurons that work as an adaptive memory as a…
In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response…
We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…
In many real-world complex systems, the time-evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here, we study opinion formation and imitation on an adaptive complex network which is dependent on…
Enabling robots to perform complex dynamic tasks such as picking up an object in one sweeping motion or pushing off a wall to quickly turn a corner is a challenging problem. The dynamic interactions implicit in these tasks are critical…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
This work introduces a general multi-level model for self-adaptive systems. A self-adaptive system is seen as composed by two levels: the lower level describing the actual behaviour of the system and the upper level accounting for the…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…