Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations

A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the attractors. A mutation introduces some new aspects: the emergence of structurally stable attractors, and chaotic itinerant behavior. In addition, it is reported that a neutral attractor can exist in the mutataion rate -> +0 region.Comment: 4 pages, 9 figure

Two-population replicator dynamics and number of Nash equilibria in random matrix games

We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed points of the dynamics and the Nash equilibria. Except for the special case of zero-sum games one finds a transition as a function of the so-called co-operation pressure between a phase in which there is a unique stable fixed point of the dynamics coinciding with a unique Nash equilibrium, and an unstable phase in which there are exponentially many Nash equilibria with statistical properties different from the stationary state of the replicator equations. Our analytical results are confirmed by numerical simulations of the replicator dynamics, and by explicit enumeration of Nash equilibria.Comment: 9 pages, 2x2 figure

Activation of lateral hypothalamus-projecting parabrachial neurons by intraorally delivered gustatory stimuli

The present study investigated a subpopulation of neurons in the mouse parabrachial nucleus (PbN), a gustatory and visceral relay area in the brainstem, that project to the lateral hypothalamus (LH). We made injections of the retrograde tracer Fluorogold (FG) into LH, resulting in fluorescent labeling of neurons located in different regions of the PbN. Mice were stimulated through an intraoral cannula with one of seven different taste stimuli, and PbN sections were processed for immunohistochemical detection of the immediate early gene c-Fos, which labels activated neurons. LH projection neurons were found in all PbN subnuclei, but in greater concentration in lateral subnuclei, including the dorsal lateral subnucleus (dl). Fos-like immunoreactivity (FLI) was observed in the PbN in a stimulus-dependent pattern, with the greatest differentiation between intraoral stimulation with sweet (0.5 M sucrose) and bitter (0.003 M quinine) compounds. In particular, sweet and umami-tasting stimuli evoked robust FLI in cells in the dl, whereas quinine evoked almost no FLI in cells in this subnucleus. Double-labeled cells were also found in the greatest quantity in the dl. Overall, these results support the hypothesis that the dl contains direct a projection to the LH that is activated preferentially by appetitive compounds; this projection may be mediated by taste and/or postingestive mechanisms

Parisi Phase in a Neuron

Pattern storage by a single neuron is revisited. Generalizing Parisi's framework for spin glasses we obtain a variational free energy functional for the neuron. The solution is demonstrated at high temperature and large relative number of examples, where several phases are identified by thermodynamical stability analysis, two of them exhibiting spontaneous full replica symmetry breaking. We give analytically the curved segments of the order parameter function and in representative cases compute the free energy, the storage error, and the entropy.Comment: 4 pages in prl twocolumn format + 3 Postscript figures. Submitted to Physical Review Letter

Species Abundance Patterns in Complex Evolutionary Dynamics

An analytic theory of species abundance patterns (SAPs) in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka-Volterra equation, with diverse interspecies interactions. Various SAPs observed in nature are derived from a single parameter. The abundance distribution is formed like a widely observed left-skewed lognormal distribution. As the model has a general form, the result can be applied to similar patterns in other complex biological networks, e.g. gene expression.Comment: 4 pages, 3 figures. Physical Review Letters, in pres

Statistical mechanics and stability of a model eco-system

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally direct competitive or co-operative interaction between species may occur through a random coupling matrix. We compute the order parameters of the system in a fixed point regime, and identify the onset of instability and compute the phase diagram. We focus on the effects of variability of resources, direct interaction between species, co-operation pressure and dilution on the stability and the diversity of the ecosystem. It is shown that resources can be exploited optimally only in absence of co-operation pressure or direct interaction between species.Comment: 23 pages, 13 figures; text of paper modified, discussion extended, references adde

Non-isothermal model for the direct isotropic/smectic-A liquid crystalline transition

An extension to a high-order model for the direct isotropic/smectic-A liquid crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase-ordering. Multi-scale multi-transport simulations of the non-isothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth, under shallow quench/undercooling conditions. Non-isothermal simulations, where meta-stable nematic pre-ordering precedes smectic-A growth, were also conducted and novel non-monotonic phase-transformation kinetics observed.Comment: First revision: 20 pages, 7 figure