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Related Concept Videos

Chemical Reactions02:26

Chemical Reactions

A balanced chemical equation provides the information of chemical formulas of the reactants and products involved in the chemical change. A reaction’s stoichiometry helps predict how much of the reactant is needed to produce the desired amount of product, or in some cases, how much product will be formed from a specific amount of the reactant.
The relative amounts of reactants and products represented in a balanced chemical equation are often referred to as stoichiometric amounts. However, in...
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A balanced chemical equation provides a great deal of information in a very succinct format. Chemical formulas provide the identities of the reactants and products involved in the chemical change, allowing classification of the reaction. Coefficients provide the relative numbers of these chemical species, allowing a quantitative assessment of the relationships between the amounts of substances consumed and produced by the reaction. These quantitative relationships are known as the reaction’s...
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Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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A Method for Measuring Metabolism in Sorted Subpopulations of Complex Cell Communities Using Stable Isotope Tracing
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Quantifying chaos for ecological stoichiometry.

Jorge Duarte1, Cristina Januário, Nuno Martins

  • 1Department of Chemistry, Mathematics Unit, ISEL-High Institute of Engineering of Lisbon, Rua Conselheiro Emídio Navarro 1, 1949-014 Lisboa, Portugal.

Chaos (Woodbury, N.Y.)
|October 5, 2010
PubMed
Summary
This summary is machine-generated.

Ecological stoichiometry can lead to chaotic coexistence between competing species. This study quantifies chaotic dynamics in a three-species food chain model, revealing how parameters influence stability and species interactions.

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Area of Science:

  • Ecology
  • Theoretical Ecology
  • Ecological Stoichiometry

Background:

  • Ecological stoichiometry examines how elemental composition affects species interactions.
  • Previous models show chaos can enable coexistence between competing consumers.
  • Species composition significantly impacts population dynamics.

Purpose of the Study:

  • To analyze topological and dynamical properties of chaotic attractors in a stoichiometric food chain model.
  • To numerically prove chaotic competitive coexistence using symbolic dynamics.
  • To investigate the influence of ecological parameters on system stability.

Main Methods:

  • Utilized symbolic dynamics to compute topological entropy from Poincaré return maps.
  • Analyzed Lyapunov exponents to confirm chaotic behavior.
  • Investigated parameter variations (δ1 and ζ) to observe bifurcation scenarios and stability changes.

Main Results:

  • Chaotic competitive coexistence was numerically proven, characterized by positive topological entropy and Lyapunov exponents.
  • Increasing the first predator's growth rate (δ1) initially promoted chaos but higher values led to stable dynamics.
  • Decreasing predator efficiency (increasing ζ) stabilized the ecological model.

Conclusions:

  • Topological and dynamical measures confirm the role of chaos in enabling species coexistence within stoichiometric constraints.
  • Parameter-dependent bifurcations dictate the transition between chaotic and stable dynamics.
  • The fractal dimension of chaotic attractors was estimated for this ecological model.