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Recent collapses of many fisheries across the globe have challenged the mathematical approach to these systems through classic bioeconomic models. Decimated populations did not recover as fast as predicted by these models and depensatory…
We study population dynamics through a general growth/degrowth-fragmentation process, with resource consumption and unbounded growth/degrowth, birth and death rates. Our model is structured in a positive trait called energy (which is a…
In the present paper, we study the Cauchy problem for the weakly coupled system of the generalized Tricomi equations with multiple propagation speeds. Our aim of this paper is to prove a small data blow-up result and an upper estimate of…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
In this paper, we mainly investigate the Cauchy problem for the periodic Phan-Thein-Tanner (PTT) model. This model is derived from network theory for the polymeric fluid. We prove that the strong solutions of PTT model will blow up in…
We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan…
Harmful cyanobacterial blooms (CBs) are increasingly prevalent worldwide, posing significant environmental and health concerns. We derive a stoichiometric model describing the population dynamics and toxicity of cyanobacteria in…
We develop a trait-based model founded on the hypothesis that biological systems evolve and organize to maximize entropy production by dissipating chemical and electromagnetic potentials over longer time scales than abiotic processes by…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
We study the Cauchy problem with small initial data for a system of semilinear wave equations $\square u = |v|^p$, $\square v = |\partial_t u|^p$ in $n$-dimensional space. When $n \geq 2$, we prove that blow-up can occur for arbitrarily…
Excitatory and inhibitory nonlinear noisy leaky integrate and fire models are often used to describe neural networks. Recently, new mathematical results have provided a better understanding of them. It has been proved that a fully…
We study the dyadic model of the Navier-Stokes equations introduced by Katz and Pavlovi\'c. They showed a finite time blow-up in the case where the dissipation degree $\alpha$ is less than 1/4. In this paper we prove the existence of weak…
Classical models of aphid population dynamics are unable to explain multi-peak patterns in field populations. We consider the variable carrying capacity model (VCM), which can generate such complex multi-peak dynamics, but is also…
We propose a model for evolutionary game dynamics with three strategies $A$, $B$ and $C$ in the framework of Moran process in finite populations. The model can be described as a stochastic process which can be numerically computed from a…
In this paper, we consider the long time behavior for the solution of a class of variable coefficient wave equation with nonlinear damping and logarithmic source. The existence and uniqueness of local weak solution can be obtained by using…
In \cite{hou}, Hou gave a compelling numerical candidate for a singular solution of the 3D Navier-Stokes equations. We pioneer classifications of potentially singular solutions, motivated by the issue of investigating the viability of…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each…
Self-triggered control (STC) is a well-established technique to reduce the amount of samples for sampled-data systems, and is hence particularly useful for Networked Control Systems. At each sampling instant, an STC mechanism determines not…
In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy…