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We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromones and interact with them through alignment interaction. The directed pheromones intend to model…
We propose a physical framework for ant navigation of chemical trails. For this, we use controlled experiments in which individuals follow narrow pheromone trails, for which ants display oscillatory motion, as previously reported in the…
With the increasing demand and complexity of networks, factors such as balancing the load, improving the performance, reducing delay and finding optimal path between nodes in a computer network have become crucial. The traditional routing…
This paper studies the asymptotic behavior of several continuous-time dynamical systems which are analogs of ant colony optimization algorithms that solve shortest path problems. Local asymptotic stability of the equilibrium corresponding…
Ant Colony Optimization (ACO) is a metaheuristic for solving difficult discrete optimization problems. This paper presents a deterministic model based on differential equation to analyze the dynamics of basic Ant System algorithm.…
In this paper, we propose a new model of chemotaxis motivated by ant trail pattern formation, formulated as a coupled parabolic-parabolic local PDE system, for the population density and the chemical field. The main novelty lies in the…
Animal movement exhibits complex behavior which can be influenced by unobserved environmental conditions. We propose a model which allows for a spatially-varying movement rate and spatially-varying drift through a semiparametric potential…
Enormous progress have been made in the last 20 years since the publication of our review \cite{csk05polrev} in this journal on transport and traffic phenomena in biology. In this brief article we present a glimpse of the major advances…
We investigate an interacting particle model to simulate a foraging colony of ants, where each ant is represented as an active Brownian particle. The interactions among ants are mediated through chemotaxis, aligning their orientations with…
We propose an active walker model for the motion of individual ants communicating via chemical signals. It is assumed that communication takes the form of a time-dependent pheromone field that feedbacks into the motion ants through…
A modified version of Langton's ant is considered. The modified automaton is allowed to go straight $N$-th step instead of turning. The cell state, however, is changed as usually. Depending on the value of $N$ the automaton exhibits…
The paper presents an exponential pheromone deposition rule to modify the basic ant system algorithm which employs constant deposition rule. A stability analysis using differential equation is carried out to find out the values of…
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…
We investigated the emerging traffic patterns of Argentine ants (Linepithema humile) as they navigated a narrow bridge between their nest and a food source. By tracking ant movements in experiments with varying bridge widths and colony…
The paper presents an exponential pheromone deposition approach to improve the performance of classical Ant System algorithm which employs uniform deposition rule. A simplified analysis using differential equations is carried out to study…
We propose and numerically analyze a PDE model of ant foraging behavior. Ant foraging is a prime example of individuals following simple behavioral rules based on local information producing complex, organized and ``intelligent'' strategies…
We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included which describes a slowing down when two…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
In this paper we analyze a system of PDEs recently introduced in [P. Amorim, {\it Modeling ant foraging: a {chemotaxis} approach with pheromones and trail formation}], in order to describe the dynamics of ant foraging. The system is made of…
We investigate the behaviour of an original traffic model. The model considers a single multi-lane street, populated by autonomous vehicles directed from either end to the other. Lanes have no intrinsic directionality, and the vehicles are…