Effect of Discrete Macroion Charge Distributions on Electric Double Layer of a Spherical Macroion

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on the structure of electric double layer (EDL) of a spherical macroion has been investigated by Monte Carlo (MC) simulations. Two discrete models have been investigated in addition to the central macroion charge: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both models have been studied with fixed and mobile macroion charges. The radial functions of local densities and electrostatic potential in EDL, are calculated and compared to the results obtained for the central macroion charge distribution. It is concluded that the model of charge distribution significantly affects the EDL structure close to the macroion, while the effect is much weaker at larger distances. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion, as a result the absolute values of surface potential ?₀ and zeta ξ potential are decreased. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the absolute values of ?₀ and ξ potentials are increased.     

The impact of constant effort harvesting on the dynamics of a discrete‐time contest competition model

In this paper, we study a general discrete‐time model representing the dynamics of a contest competition species with constant effort exploitation. In particular, we consider the difference equation x _{n +1}=x _n f (x _{n ?k} )?h x _n where h >0, k ∈{0,1}, and the density dependent function f satisfies certain conditions that are typical of a contest competition. The harvesting parameter h is considered as the main parameter, and its effect on the general dynamics of the model is investigated. In the absence of delay in the recruitment (k =0), we show the effect of h on the stability, the maximum sustainable yield, the persistence of solutions, and how the intraspecific competition change from contest to scramble competition. When the delay in recruitment is 1 (k =1), we show that a Neimark‐Sacker bifurcation occurs, and the obtained invariant curve is supercritical. Furthermore, we give a characterization of the persistent set.     

Convergence to periodic solutions

Open Problems and Conjectures Edited by Gerry Ladas In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas     

Patterns of boundedness of a rational system in the plane

We investigate the boundedness character of non-negative solutions of a rational system in the plane. The system contains 10 parameters with non-negative real values and consists of 343 special cases, each with positive parameters. In 342 out of the 343 special cases, we establish easily verifiable necessary and sufficient conditions, explicitly stated in terms of 10 parameters, which determine the boundedness character of solutions of the system. In the remaining special case, we conjecture the boundedness character of solutions. It is interesting to note that this special case can be transformed to the well-known May's Host-Parasitoid model.     

On a Class of Difference Equations with Strong Negative Feedback

We investigate the behavior of the positive solutions of a class of difference equations with strong negative feedback. In particular we show that the positive equilibrium is globally asymptotically stable.