@article {2022,
	title = {Mathematical modelling of oscillating patterns for chronic autoimmune diseases},
	journal = {Mathematical Methods in the Applied SciencesMathematical Methods in the Applied SciencesMath Meth Appl Sci},
	volume = {n/a},
	year = {2022},
	month = {2022/04/01},
	abstract = {<p>Many autoimmune diseases are chronic in nature, so that in general, patients experience periods of recurrence and remission of the symptoms characterizing their specific autoimmune ailment. In order to describe this very important feature of autoimmunity, we construct a mathematical model of kinetic type describing the immune system cellular interactions in the context of autoimmunity exhibiting recurrent dynamics. The model equations constitute a nonlinear system of integro-differential equations with quadratic terms that describe the interactions between self-antigen presenting cells, self-reactive T cells, and immunosuppressive cells. We consider a constant input of self-antigen presenting cells, due to external environmental factors that are believed to trigger autoimmunity in people with predisposition for this condition. We also consider the natural death of all cell populations involved in our model, caused by their interaction with cells of the host environment. We derive the macroscopic analogue and show positivity and well-posedness of the solution and then we study the equilibria of the corresponding dynamical system and their stability properties. By applying dynamical system theory, we prove that steady oscillations may arise due to the occurrence of a Hopf bifurcation. We perform some numerical simulations for our model, and we observe a recurrent pattern in the solutions of both the kinetic description and its macroscopic analogue, which leads us to conclude that this model is able to capture the chronic behaviour of many autoimmune diseases.</p>},
	keywords = {autoimmune diseases, cellular interactions, Dynamical systems, Hopf bifurcation, kinetic theory, mathematical biology},
	isbn = {0170-4214},
	url = {https://doi.org/10.1002/mma.8229},
	author = {Rossella Della Marca and Maria da Piedade Machado Ramos and Carolina Ribeiro and Ana Jacinta Soares}
}
@article {AGOSTINELLI2019103702,
	title = {Nutations in growing plant shoots: The role of elastic deformations due to gravity loading},
	journal = {Journal of the Mechanics and Physics of Solids},
	year = {2019},
	pages = {103702},
	abstract = {<p>The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin{\textquoteright}s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.</p>},
	keywords = {Circumnutations, Flutter instability, Gravitropism, Hopf bifurcation},
	issn = {0022-5096},
	doi = {10.1016/j.jmps.2019.103702},
	url = {https://doi.org/10.1016/j.jmps.2019.103702},
	author = {Daniele Agostinelli and Alessandro Lucantonio and Giovanni Noselli and Antonio DeSimone}
}
