We address the biological dynamics problem of the persistence of several species in conditions of non-existence of an equilibrium, including an example of stabilization by predation and the very controversial “competitive exclusion”. We give normal forms for various examples of such persistence and comments on the involved topology, which implies the presence of exceptional heteroclinic connections binding equilibria on the boundary.

WHO II low grade glioma evolves inevitably to anaplastic transformation. Magnetic resonance imaging is a good non-invasive way to watch it, by hemodynamic and metabolic modifications, thanks to multinuclear spectroscopy 1H/31P. In this work we study a multi-scale minimal model of hemodynamics and metabolism applied to the study of gliomas. This mathematical analysis leads us to a fast-slow system. The control of the position of the stationary point brings to the concept of domain of viability. Starting from this system, the (...) equations bring to light the parameters that push glioma cells out of their domain of viability. Four fundamental factors are highlighted. The first two are cerebral blood flow and the rate of lactate transport through monocarboxylate transporters, which must be reduced in order to push glioma out of its domain of viability. Another factor is the intra arterial lactate, which must be increased. The last factor is pH, indeed a decrease of intra cellular pH could interfere with glioma growth. These reflections suggest that these four parameters could lead to new therapeutic strategies for the management of low grade gliomas. (shrink)

The present work is a contribution to the understanding of the sempiternal problem of the “burden of factor two” implied by sexual reproduction versus asexual one, as males are energy consumers not contributing to the production of offspring. We construct a deterministic mathematical model in population dynamics where a species enjoys both sexual and parthenogenetic capabilities of reproduction and lives on a limited resource. We then show how polygamy implies instability of a parthenogenetic population with a small number of sexually (...) born males. This instability implies evolution of the system towards an attractor involving both populations. We also exhibit the analogy with a parasite/host system. (shrink)

We investigate a system of two species exploiting a common resource. We consider both abiotic and biotic resources. We are interested in the asymmetric competition where a given consumer is the locally superior resource exploiter and the other is the locally inferior resource exploiter. They also interact directly via interference competition in the sense that LIE individuals can use two opposite strategies to compete with LSE individuals: we assume, in the first case, that LIE uses an avoiding strategy, i.e. LIE (...) individuals go to a non-competition patch to avoids competition with LSE individuals, and in the second one, LIE uses an aggressive strategy, i.e. being very aggressive so that LSE individuals have to go to a non-competition patch. We further assume that there is no resource in the non-competition patch so that individuals have to come back to the competition patch for their maintenance, and the migration process acts on a fast time scale in comparison with demography and competition processes. The models show that being aggressive is efficient for LIE’s survival and even provoke global extinction of the LSE and this result does not depend on the nature of resource. (shrink)

This work presents a mathematical model describing the interactions between the cross-shore structure of small pelagic fish population an their exploitation by coastal and offshore fisheries. The complete model is a system of seven ODE’s governing three stocks of small pelagic fish population moving and growing between three zones. Two types of fishing fleets are inter-acting with the fish population, industrial boats, constrained to offshore area, and artisanal boats, operating from the shore. Two time scales were considered and we use (...) aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model, which is a four dimension one. The analysis of the aggregated model is performed. We discuss the possible equilibriums and their meaning in terms of fishery management. An interesting equilibrium state can be obtained for which we can expect coexistence and a stable equilibrium state between fish stocks and fishing efforts. Some identification parameters are also given in the discussion part of the model. (shrink)

Blood coagulation is regulated through a complex network of biochemical reactions of blood factors. The main acting enzyme is thrombin whose propagation in blood plasma leads to fibrin clot formation. Spontaneous clot formation is normally controlled through the action of different plasma inhibitors, in particular, through the thrombin binding by antithrombin. In the current study we develop a mathematical model of clot formation both in quiescent plasma and in blood flow and determine the analytical conditions on the antithrombin concentration corresponding (...) to different regimes of blood coagulation. (shrink)

The French school of theoretical biology has been mainly initiated in Poitiers during the sixties by scientists like J. Besson, G. Bouligand, P. Gavaudan, M. P. Schützenberger and R. Thom, launching many new research domains on the fractal dimension, the combinatorial properties of the genetic code and related amino-acids as well as on the genetic regulation of the biological processes. Presently, the biological science knows that RNA molecules are often involved in the regulation of complex genetic networks as effectors, e.g., (...) activators, inhibitors or hybrids. Examples of such networks will be given showing that there exist RNA “relics” that have played an important role during evolution and have survived in many genomes, whose probability distribution of their sub-sequences is quantified by the Shannon entropy, and the robustness of the dynamics of the networks they regulate can be characterized by the Kolmogorov–Sinaï dynamic entropy and attractor entropy. (shrink)