Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment

A three-species non-autonomous stochastic Lotka–Volterra food web system in a polluted environment is proposed, and the existence of positive periodic solutions of this system is established by constructing a proper Lyapunov function. Then the extinction property and its threshold between persistence and extinction are discussed by using Itô’s formula and the strong law of large numbers of martingale, and the sufficient condition of a.s. exponential stability of equilibrium point is obtained. Finally, the conclusions are tested by several numerical simulations.

Extinction of a two species competitive stage-structured system with the effect of toxic substance and harvesting

The extinction property of a two species competitive stage-structured phytoplankton system with harvesting is studied in this paper. Several sets of sufficient conditions which ensure that one of the components will be driven to extinction are established. Our results supplement and complement the results of Li and Chen [Extinction in periodic competitive stage-structured Lotka-Volterra model with the effects of toxic substances, J. Comput. Appl. Math., 2009, 231(1), 143-153] and Liu, Chen, Luo et al. [Extinction and permanence in nonautonomous competitive system with stage structure, J. Math. Anal. Appl., 2002, 274(2), 667-684].

Anisotropically Shaped Magnetic/Plasmonic Nanocomposites for Information Encryption and Magnetic-Field-Direction Sensing

Instantaneous control over the orientation of anisotropically shaped plasmonic nanostructures allows for selective excitation of plasmon modes and enables dynamic tuning of the plasmonic properties. Herein we report the synthesis of rod-shaped magnetic/plasmonic core-shell nanocomposite particles and demonstrate the active tuning of their optical property by manipulating their orientation using an external magnetic field. We further design and construct an IR-photoelectric coupling system, which generates an output voltage depending on the extinction property of the measured nanocomposite sample. We employ the device to demonstrate that the nanocomposite particles can serve as units for information encryption when immobilized in a polymer film and additionally when dispersed in solution can be employed as a new type of magnetic-field-direction sensor.

On the Roughness of Quasinilpotency Property of One-parameter Semigroups

Let S := {S(t)}t≥0 be a C0-semigroup of quasinilpotent operators (i.e., σ(S(t)) = {0} for eacht> 0). In dynamical systems theory the above quasinilpotency property is equivalent to a very strong concept of stability for the solutions of autonomous systems. This concept is frequently called superstability and weakens the classical ûnite time extinction property (roughly speaking, disappearing solutions). We show that under some assumptions, the quasinilpotency, or equivalently, the superstability property of a C0-semigroup is preserved under the perturbations of its infinitesimal generator.

Dynamic Behaviors of a Discrete Periodic Predator-Prey-Mutualist System

A nonautonomous discrete predator-prey-mutualist system is proposed and studied in this paper. Sufficient conditions which ensure the permanence and existence of a unique globally stable periodic solution are obtained. We also investigate the extinction property of the predator species; our results indicate that if the cooperative effect between the prey and mutualist species is large enough, then the predator species will be driven to extinction due to the lack of enough food. Two examples together with numerical simulations show the feasibility of the main results.