相关论文: Asymptotic behavior for a non-autonomous model of …

The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…

In this paper we analyze a model for electroporation, a biological process in which a cell membrane exposed to an external voltage becomes permeable due to the formation and growth of nanoscale membrane pores. We prove a local stability…

We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a…

Grounding autonomous behavior in the nervous system is a fundamental challenge for neuroscience. In particular, the self-organized behavioral development provides more questions than answers. Are there special functional units for…

Living organisms must actively maintain themselves in order to continue existing. Autopoiesis is a key concept in the study of living organisms, where the boundaries of the organism is not static by dynamically regulated by the system…

Many complex adaptive systems contain a large diversity of specialized components. The specialization at the level of the microscopic degrees of freedom, and diversity at the level of the system as a whole are phenomena that appear during…

We consider evolution equations of the form \begin{equation*}\label{Abstract equation} \dot u(t)+ A(t)u(t)=0,\ \ t\in[0,T],\ \ u(0)=u_0, \end{equation*} where $A(t),\ t\in [0,T],$ are associated with a non-autonomous sesquilinear form…

When modeling multivariate phenomena, properly capturing the joint extremal behavior is often one of the many concerns. Archimax copulas appear as successful candidates in case of asymptotic dependence. In this paper, the class of Archimax…

To study the interaction between retinal stimulation by redundant geometrical patterns and the cortical response in the primary visual cortex (V1), we focus on the MacKay effect (Nature, 1957) and Billock and Tsou's experiments (PNAS,…

This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…

This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…

We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…

The reward system is one of the fundamental drivers of animal behaviors and is critical for survival and reproduction. Despite its importance, the problem of how the reward system has evolved is underexplored. In this paper, we try to…

This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. We establish rough exponential asymptotic…

A non-autonomous evolution semi-linear differential system under non-instantaneous impulses, delays, and perturbed by non-local conditions is studied. Its piece-wise continuous solutions belong to a finite-dimensional Banach space. The…

In this article, we show that a technique for showing well-posedness results for evolutionary equations in the sense of [13] established in [16] applies to a broader class of non-autonomous integro-differential-algebraic equations. Using…

The evolutionary balance between innate and learned behaviors is highly intricate, and different organisms have found different solutions to this problem. We hypothesize that the emergence and exact form of learning behaviors is naturally…

Most theories of behavior posit that agents tend to maximize some form of reward or utility. However, animals very often move with curiosity and seem to be motivated in a reward-free manner. Here we abandon the idea of reward maximization,…