The atomic force microscope system (AFM) has become a popular and useful instrument to measure the intermolecular forces with atomic resolution that can be applied in electronics, biological analysis, materials, semiconductors, etc. This paper studies the bifurcation phenomenon and complex nonlinear dynamic behavior of the probe tip between the sample and microcantilever of an atomic force micr...

This paper explores log-periodicity in a forest-fire cellular-automata model. At each time step of this model a tree is dropped on a randomly chosen site; if the site is unoccupied, the tree is planted. Then, for a given sparking frequency, matches are dropped on a randomly chosen site; if the site is occupied by a tree, the tree ignites and an “instantaneous” model fire consumes that tree and ...

The purpose of this project is to model multi-species interactions using Volterra-Lotka equations in both two and three dimensions. Changes in population dynamics that arise as a result of modifying parameters are examined. The population dynamics of the resulting systems are analyzed in terms of stability around equilibrium points and within invariant surfaces. Of particular interest is period...

We consider a system of differential equations the behavior of which solutions possesses several properties characteristic of the blood pressure distribution. The system can be used for a compartmental modeling [8, 15] of the cardiovascular system. It admits a unique bounded solution such that all coordinates of the solution are separated from zero by positive numbers, and which is periodic, ev...

We design a partially aperiodic, vertically-aligned silicon nanowire array that maximizes photovoltaic absorption. The optimal structure is obtained using a random walk algorithm with transfer matrix method based electromagnetic forward solver. The optimal, aperiodic structure exhibits a 2.35 times enhancement in ultimate efficiency compared to its periodic counterpart. The spectral behavior mi...

This paper presents a simple nonautonomous circuit with a periodic pulse-train input. If the input does not exist, the circuit exhibits either equilibrium attractor or hard oscillation. If a periodic pulse-train input is applied, the circuit exhibits interesting chaotic and periodic attractors. The circuit behavior can be analyzed by a mapping procedure based on a 1-D return map focusing on the...

By constructing a suitable Lyapunov functional and using almost periodic functional hull theory, we study the almost periodic dynamic behavior of a discrete Leslie-Gower predator-prey model with constant and variable delays. Based on the permanence result, sufficient conditions are established for the existence and uniqueness of globally attractive almost periodic solution. A example and a nume...

Recently, there has been a great interest in studying the periodic nature of nonlinear difference equations. Although difference equations are relatively simple in form, it is, unfortunately, extremely difficult to understand thoroughly the periodic behavior of their solutions. The periodic nature of nonlinear difference equations of the max type has been investigated by many authors. See, for ...

During mother-infant face-to-face interactions, bidirectional influence could be achieved through either the entraining of periodic cycles in the behavior of each partner or through the stochastic organization of behaviors. To determine whether and how bidirectional influence occurs, we used both timeand frequency-domain techniques to study the interactions of 54 mother-infant pairs, 18 each at...

The analysis of potentially chaotic behavior in biological and biomedical phenomena has attracted great interest in recent years (1–6). Although no universally accepted mathematical definition of the term chaos exists, Strogatz (7) provides a working definition as ‘‘aperiodic long-term behavior in a deterministic system that exhibits sensitive dependence on initial conditions.’’ Aperiodic long-...