Size- and position-dependent bifurcations of chemical microoscillators in confined geometries

Reversible chemical reactions model with fractional difference operator: Dynamical analysis and synchronization

Chemical reactions form the basis of life and understanding the different patterns and unpredictable changes in the reactions are noteworthy in real life situations. The article aims at constructing a mathematical model of two step reversible chemical reactions with a Caputo fractional difference operator. The reversible reaction involves the breakdown of an ester compound in the presence of water followed by the formation of fatty acid salts from the reaction of a free fatty acid with alkali hydroxide, such as NaOH. Using bifurcation diagrams, the chaotic response exhibited by the system is illustrated for state variables with identical fractional order and variables with non-identical fractional orders. The changes in periodic states of the system are investigated for each state variables with time varying plots and maximum Lyapunov exponents using the Jacobian matrix method are presented in support of the bifurcation diagrams. The synchronization of the subsystems of the proposed system is achieved with nonlinear control functions. Numerical simulations are presented to provide comparison of commensurate and incommensurate order models. Understanding the nature of these processes has significant applications in the production of bio-fuels from vegetable oils and animal fats by a transesterification reaction.

Modeling of Astrocyte Networks: Toward Realistic Topology and Dynamics

Neuronal firing and neuron-to-neuron synaptic wiring are currently widely described as orchestrated by astrocytes—elaborately ramified glial cells tiling the cortical and hippocampal space into non-overlapping domains, each covering hundreds of individual dendrites and hundreds thousands synapses. A key component to astrocytic signaling is the dynamics of cytosolic Ca²⁺ which displays multiscale spatiotemporal patterns from short confined elemental Ca²⁺ events (puffs) to Ca²⁺ waves expanding through many cells. Here, we synthesize the current understanding of astrocyte morphology, coupling local synaptic activity to astrocytic Ca²⁺ in perisynaptic astrocytic processes and morphology-defined mechanisms of Ca²⁺ regulation in a distributed model. To this end, we build simplified realistic data-driven spatial network templates and compile model equations as defined by local cell morphology. The input to the model is spatially uncorrelated stochastic synaptic activity. The proposed modeling approach is validated by statistics of simulated Ca²⁺ transients at a single cell level. In multicellular templates we observe regular sequences of cell entrainment in Ca²⁺ waves, as a result of interplay between stochastic input and morphology variability between individual astrocytes. Our approach adds spatial dimension to the existing astrocyte models by employment of realistic morphology while retaining enough flexibility and scalability to be embedded in multiscale heterocellular models of neural tissue. We conclude that the proposed approach provides a useful description of neuron-driven Ca²⁺-activity in the astrocyte syncytium.

Distance dependent types of coupling of chemical micro-oscillators immersed in a water-in-oil microemulsion

A system of micro-spheres immersed in a water-in-oil microemulsion (ME) is studied both theoretically and experimentally.