Quantifying chaos for ecological stoichiometry

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincareacute return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing delta(1). However, for higher values of delta(1) the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter zeta) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Solution enthalpies of 1,4-dioxane: Study of solvent effects through quantitative structure-property relationships

Solution enthalpies of 1,4-dioxane have been obtained in 15 protic and aprotic solvents at 298.15 K. Breaking the overall process through the use of Solomonov's methodology the cavity term was calculated and interaction enthalpies (Delta H-int) were determined. Main factors involved in the interaction enthalpy have been identified and quantified using a QSPR approach based on the TAKA model equation. The relevant descriptors were found to be pi* and beta, which showed, respectively, exothermic and endothermic contributions. The magnitude of pi* coefficient points toward non-specific solute-solvent interactions playing a major role in the solution process. The positive value of the beta coefficient reflects the endothermic character of the solvents' hydrogen bond acceptor (HBA) basicity contribution, indicating that solvent molecules engaged in hydrogen bonding preferentially interact with each other rather than with 1,4-dioxane. (C) 2013 Elsevier B.V. All rights reserved.

Use of quantitative structure-property relationships to study the solvation process of 18-crown-6

Solution enthalpies of 18-crown-6 have been obtained for a set of 14 protic and aprotic solvents at 298.15 K. The complementary use of Solomonov's methodology and a QSPR-based approach allowed the identification of the most significant solvent descriptors that model the interaction enthalpy contribution of the solution process (Delta H-int(A/S)). Results were compared with data previously obtained for 1,4-dioxane. Although the interaction enthalpies of 18-crown-6 correlate well with those of 1,4-dioxane, the magnitude of the most relevant parameters, pi* and beta, is almost three times higher for 18-crown-6. This is rationalized in terms of the impact of the solute's volume in the solution processes of both compounds. (C) 2015 Elsevier B.V. All rights reserved.