In this paper, using the theories and methods of ecology and ordinary differential equations, an ecological model with an impulsive control strategy and a distributed time delay is defined. Using the theory of the impulsive equation, small-amplitude perturbations, and comparative techniques, a condition is identified which guarantees the global asymptotic stability of the prey-(x) and predator-...

Current cocaine treatments may be enhanced with a better understanding of the underlying mechanisms that contribute to the onset and maintenance of the disease, such as life stress and impulsivity. Life stress and impulsivity have previously been studied independently as contributors to drug use, and the current study expands upon past research by examining how these factors interact with one a...

Behavioral-economic studies have shown that differences between lean and obese Zuckers in food consumption depend on the response requirement for food. Since a response requirement inherently increases the delay to reinforcement, differences in sensitivity to delay may also be a relevant mechanism of food consumption in the obese Zucker rat. Furthermore, the endocannabinoid neurotransmitter sys...

The attractivity of nonlinear differential equations with time delays and impulsive effects is discussed. We obtain some criteria to determine the attracting set and attracting basin of the impulsive delay system by developing an impulsive delay differential inequality and introducing the concept of nonlinear measure. Examples and their simulations illustrate the effectiveness of the results an...

In this paper, we establish the existence of local and global mild solution for an impulsive fractional integro-differential equation with state dependent delay subject to nonlocal initial condition. The existence results for local mild solution are proved by applying the Schauder, nonlinear Larey Schauder alternative and Banach fixed point theorems. Then, we prove global existence result. An e...

This paper considers the global exponential stability of delay neural networks with impulsive perturbations. By establishing a new impulsive delay inequality which is different from the earlier publication, we obtain some new sufficient conditions ensuring exponential stability of the equilibrium point for such neural networks. The neural networks model considered include the impulsive delay Ho...

In this paper, we prove the existence of mild solutions for a first order impulsive neutral evolution differential inclusion with state-dependent delay. We transform it into an integral equation and use a fixed point theorem for condensing multi-valued maps. As an application of the main theorem, we consider the case when the multi-valued nonlinearity has sub-linear growth in the state variable.

We study the existence of mild solutions for a class of impulsive fractional partial neutral stochastic integro-differential inclusions with statedependent delay. We assume that the undelayed part generates a solution operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for...

This paper is concerned with the impulsive delay differential equations with positive and negative coefficients  x′(t) + p(t)x(t− τ)− q(t)x(t− σ) = 0, t ≥ t0, t 6= tk, x(tk) = bkx(tk ) + (1− bk) (∫ tk tk−τ p(s+ τ)x(s)ds − ∫ tk tk−σ q(s+ σ)x(s)ds ) , k = 1, 2, 3, · · · . Sufficient conditions are obtained for every solution of the above equation tends to a constant as t→∞.

The nucleus accumbens core (NAc) has long been recognized as an important contributor to the computation of reward value that is critical for impulsive choice behavior. Impulsive choice refers to choosing a smaller-sooner (SS) over a larger-later (LL) reward when the LL is more optimal in terms of the rate of reward delivery. Two experiments examined the role of the NAc in impulsive choice and ...