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The global dynamics and regularity of parabolic-hyperbolic systems is an interesting topic in PDEs due to the coupling of competing dissipation and hyperbolic effects. This paper is concerned with the Cauchy problem of a…
We propose a new mathematical model for the interaction of skin cell populations with fibroblast growth factor and bone morphogenetic protein, occurring within deformable porous media. The equations for feather primordia pattering are based…
In this paper, a novel swarm intelligent algorithm is proposed called ant nesting algorithm (ANA). The algorithm is inspired by Leptothorax ants and mimics the behavior of ants searching for positions to deposit grains while building a new…
We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular…
Many ant species employ distributed population density estimation in applications ranging from quorum sensing [Pra05], to task allocation [Gor99], to appraisal of enemy colony strength [Ada90]. It has been shown that ants estimate density…
This thesis presents the theoretical, conceptual and methodological aspects that support the modeling of dynamical systems (DS) by using several agents. The modeling approach permits the assessment of properties representing order, change,…
This paper presents a system of stochastic differential equations (SDEs) as mathematical model to describe the spatial-temporal dynamics of predator-prey system in an artificial aquatic environment with schooling behavior imposed upon the…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
In this paper, we address the large-scale shepherding control problem using a continuification-based strategy. We consider a scenario in which a large group of follower agents (targets) must be confined within a designated goal region…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
We consider an agro-ecologically motivated coupling between a prey-predator system and a vector-borne epidemic system. The coupled system contains one ODE, two reaction-diffusion PDEs and one reaction-diffusionadvection PDE; it has no…
A delayed, discrete-time, prey-predator model with Allee effects imposed on prey and predator populations is defined, and dynamics of the system is characterized computationally. The parametric conditions for local asymptotic stability of…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
Drawing on the understanding of the logistic map, we propose a simple predator-prey model where predators and prey adapt to each other, leading to the co-evolution of the system. The special dynamics observed in periodic windows contribute…
Ecological modelling of increasingly more complex microbial populations is necessary to reflect the highly functional and diverse behaviour inherent to many systems found in reality. Anaerobic digestion is one such process that has…
We establish Extended Thermodynamics (ET) of rarefied polyatomic gases with six independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. The…
Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and…
Consider the Ants Nearby Treasure Search (ANTS) problem introduced by Feinerman, Korman, Lotker, and Sereni (PODC 2012), where $n$ mobile agents, initially placed at the origin of an infinite grid, collaboratively search for an…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of different dimensions, with exchange boundary conditions.…