Related papers: Introduction to Delay Models and Their Wave Soluti…
The delayed logistic equation (also known as Hutchinson's equation or Wright's equation) was originally introduced to explain oscillatory phenomena in ecological dynamics. While it motivated the development of a large number of mathematical…
Issues of resonance that appear in non-standard random walk models are discussed. The first walk is called repulsive delayed random walk, which is described in the context of a stick balancing experiment. It will be shown that a type of…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…
To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that…
The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay…
In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
Currents can affect the evolution of waves in nearshore regions through altering their wavenumber and amplitude. Including the effect of ambient currents (e.g., tidal and wind-driven) on waves in phase-resolving wave models is not…
We propose an alternative delayed population growth difference equation model based on a modification of the Beverton-Holt recurrence, assuming a delay only in the growth contribution that takes into account that those individuals that die…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the…
A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…