Research

My research focuses on nonlinear behaviors in population dynamics.

Interacting populations: I am interested in modeling behaviors and interactions among populations on different scales, from ecology to neuroscience, and studying how they shape the structure, stability, and functions of the system.

Nonlinear dynamics: When two populations coexist in the same territory, the total population (density, activity) is not simply the sum of the two. These populations can interfere with each other, cooperate, or compete for resources, or even crossbreed and reproduce. The dynamics of the whole system are derived from nonlinear interactions. Dynamical systems are useful tools to model and analyze the nonlinear behaviors of populations.

In ecology, the spread of invasive species can be affected by interactions with other species, e.g., predators or biological control agents. Mosquito controls

often rely on releasing large numbers of mosquitoes reared in the laboratory,which are either sterile or incapable of transmitting disease, to mate with wild mosquitoes and reduce their reproductive and vectorial capacity. The control succeeds if the indigenous population is replaced or eliminated, which corresponds to certain steady states of the dynamical systems used to model the population dynamics.

Excitatory and inhibitory neurons are two fundamental types of nerve cells that regulate information in the brain and nervous system. They are organized into networks that interact to produce complex patterns of activity. Neural circuits maintain a balance between excitation and inhibition to ensure that brain activity is neither too excitable nor too suppressed. Dynamical models of neural circuits could help explain the neural mechanisms underlying various

behaviors, such as brain rhythms, sensory and motion perceptions, and memory.

Spatio-temporal dynamics: Population dynamics not only change over time but also propagate over space, which leads to interesting mathematical challenges, in terms of both modelling strategies and subsequent analysis. Spatial distributions with nonlinearities allow the models to exhibit traveling waves, bumps, and other interesting patterns. I am interested in spatial models and their applications in ecology and neuroscience.

Publications

[3] P-A. Bliman, N. Nguyen, N. Vauchelet. Efficacy of the Sterile Insect Technique in the presence of inaccessible areas: A study using two-patch models (2024), Mathematical Biosciences, Volume 377.

[2] A. Leculier, N. Nguyen. A control strategy for the Sterile Insect Technique using exponentially decreasing releases to avoid the hair-trigger effect (2023), Mathematical Modelling of Natural Phenomena, Volume 18. EDP Science.

[1] L. Almeida, P-A. Bliman, N. Nguyen, N. Vauchelet. Steady-state solutions for a reaction-diffusion equation with Robin boundary conditions: Application to the control of dengue vectors (2023), European Journal of Applied Mathematics, Volume 35, Issue 3.

Authors' names appear in alphabetical order

THESIS

N. Nguyen. Spatial modeling of invasion dynamics: applications to biological control of Aedes spp. (Diptera culicidae). PhD Thesis, University Sorbonne Paris Nord (2024).

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