Book review: Elliot Murphy, The Oscillatory Nature of Language. Cambridge: Cambridge University Press, 2020. Pp. xiii + 321

Book review accepted in Journal of Linguistics.

On the Oscillatory Behavior of Some Qeneralized Differential Equation

In this article, using the Riccati-type transformation, we study the oscillatory nature of the solutions of the generalized differential equation and give some criteria of the Kamenev type that generalizes several well-known results on the topic.

Bifurcation control of a minimal model of marine plankton interaction with multiple delays

Plankton blooms and its control is an intriguing problem in ecology. To investigate the oscillatory nature of blooms, a two-dimensional model for plankton species is considered where one species is toxic phytoplankton and other is zooplankton. The delays required for the maturation time of zooplankton, the time for phytoplankton digestion and the time for phytoplankton cells to mature and release toxic substances are incorporated and the delayed model is analyzed for stability and bifurcation phenomena. It proves that periodic plankton blooms can occur when the delay (the sum of the above three delays) changes and crosses some threshold values. The phenomena described by this mechanism can be controlled through the toxin release rates of phytoplankton. Then, a delay feedback controller with the coefficient depending on delay is introduced to system. It concludes that the onset of the bifurcation can be delayed as negative feedback gain (the decay rate) decreases (increases). Some numerical examples are given to verify the effectiveness of the delay feedback control method and the existence of crossing curve. These results show that the oscillatory nature of blooms can be controlled by human behaviors.

Investigating the quasi-oscillatory behavior of electrical parameters with the concentration of D-glucose in aqueous solution

The impedance, capacitance and conductance of deionized water-glucose polar solution is measured by employing impedance spectroscopy and a quasi-oscillatory nature of variation with glucose content in the solution is observed. Such quasi-oscillatory nature is attributed to the randomly distributed water-water, water-glucose and glucose-glucose dipole interactions at the molecular level in the solution. A relevant analytical model is developed on the basis of such random distribution of the molecular dipoles and the experimental data agree well with those obtained from the theoretical model. The electrical parameters are measured in the frequency range of 100Hz to 4MHz for the volume fractions of glucose with respect to water in the range of 0.1 to 0.5. The impedance, capacitance and conductance are obtained to be in the range of 1.03 kΩ – 112 kΩ, 34.9 pF – 1.66 nF, and 8.95 μS – 52.9 μS respectively for the glucose volume fraction range considered.