Effects of US intensity during previous discrete delay conditioning on conditioned acceleration during avoidance extinction.

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

Download Full-text

Intertrial unconditioned stimuli preferentially interfere with delay conditioning.

Journal of Experimental Psychology Animal Behavior Processes ◽

10.1037/a0016922 ◽

2010 ◽

Vol 36 (2) ◽

pp. 232-242 ◽

Cited By ~ 2

Author(s):

Douglas A. Williams ◽

Heather K. MacKenzie ◽

Kenneth W. Johns

Keyword(s):

Delay Conditioning

Download Full-text

Dynamical Behavior of a Malaria Model with Discrete Delay and Optimal Insecticide Control

Biophysical Reviews and Letters ◽

10.1142/s1793048017500023 ◽

2017 ◽

Vol 12 (01) ◽

pp. 19-38 ◽

Cited By ~ 3

Author(s):

Tuhin Kumar Kar ◽

Soovoojeet Jana

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Basic Reproduction Number ◽

Human Population ◽

Reproduction Number ◽

Dynamical Behavior ◽

Control Variable ◽

Discrete Delay ◽

Insecticide Control

In this paper we have proposed and analyzed a simple three-dimensional mathematical model related to malaria disease. We consider three state variables associated with susceptible human population, infected human population and infected mosquitoes, respectively. A discrete delay parameter has been incorporated to take account of the time of incubation period with infected mosquitoes. We consider the effect of insecticide control, which is applied to the mosquitoes. Basic reproduction number is figured out for the proposed model and it is shown that when this threshold is less than unity then the system moves to the disease-free state whereas for higher values other than unity, the system would tend to an endemic state. On the other hand if we consider the system with delay, then there may exist some cases where the endemic equilibrium would be unstable although the numerical value of basic reproduction number may be greater than one. We formulate and solve the optimal control problem by considering insecticide as the control variable. Optimal control problem assures to obtain better result than the noncontrol situation. Numerical illustrations are provided in support of the theoretical results.

Download Full-text