Instability criteria for impulsive hybrid state dependent delay integrodifferential systems

In this paper, we present the sufficient conditions ensuring the instability of the zero solution of an impulsive state dependent delay integrodifferential system for different conditions on the delay function. We assume the instability of the associated linear impulsive system and apply the idea of dichotomies together with Schauder–Tychonoff theorem to establish the sufficient conditions for the unstable solution of the problem.     

Manganese-doped zinc sulfide binary nanostructures as binder-free electrode materials for supercapattery

Journal of Solid State Electrochemistry - Binary metal sulfide–based electrode materials with distinct nanoarchitecture, improved conductivities, and fascinating mechanical stabilities are...     

Nonlinear absorption properties correlated with the surface and structural changes of ultra short pulse laser irradiated CR-39

We have investigated femtosecond laser irradiation effects on the surface topography, structural changes and nonlinear absorption properties of CR-39. For this purpose, a CR-39 target was exposed in air to 25 fs, 800 nm Ti: sapphire laser radiation at fluences ranging from 0.25 J cm⁻² to 3.6 J cm⁻². The surface of irradiated CR-39 probed by an Atomic Force Microscope (AFM) exhibits the formation of several topographical structures, like bumps, explosions and nano cavities. Raman spectroscopy is performed to explore chemical and structural modification of the irradiated target. The spectroscopy reveals changes such as cross linking, bond breaking, formation of new bonds etc. in the fundamental structure of the polymer after irradiation. In order to establish a correlation between morphological and structural changes with the changes in the nonlinear absorption of the irradiated CR-39, a Z-scan technique was employed. A comparison of experimentally obtained data from Z-scan measurements with our calculations predicts the dominance of three-photon absorption in the case of pristine CR-39, whereas for irradiated targets concurrence of three- and two-photon absorption is probable. Nonlinear absorption increases with increasing laser fluences and is well correlated by surface and structural changes revealed by AFM and Raman spectroscopy.     

Dynamical behavior of a stochastic predator-prey model with stage structure for prey

Abstract

In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases. Some examples and numerical simulations are carried out to validate our analytical findings.     

Fractional order nonlinear mixed coupled systems with coupled integro-differential boundary conditions

We study the existence and uniqueness of solutions for a class of coupled fractional differential equations involving both Riemann-Liouville and Caputo fractional derivatives, and coupled integro-differential boundary conditions. We derive the desired results with the aid of modern methods of functional analysis. An example illustrating the abstract results is also presented.     

Dynamical behavior of a stochastic food chain chemostat model with Monod response functions

This paper studies a food chain chemostat model with Monod response functions, which is perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then sufficient conditions for the existence of a unique ergodic stationary distribution are established by constructing suitable Lyapunov functions. Moreover, we consider the extinction of microbes in two cases. In the first case, both the predator and prey species are extinct. In the second case, only the predator species is extinct, and the prey species survives. Finally, numerical simulations are carried out to illustrate the theoretical results.     

Existence and approximation of solutions of forced duffing type integro-differential equations with three-point nonlinear boundary conditions

A generalized quasilinearization technique is developed to obtain an analytic approximation of the solutions of the forced Duffing type integro-differential equation with nonlinear three-point boundary conditions. Monotone sequences of approximate solutions converging uniformly and quadratically to a unique solution of the problem are presented.