This note is a slightly revised version of an earlier note with the same title that was part of a larger research project of the Dynamical Systems Group at Ohio University. While the major findings of the project are described in [1], this note complements [1] as it contains a more extensive review of some basic low-dimensional examples of Boolean systems and their ODE counterparts and explores...

The multiplication by a constant (say, by 2) acts on the set Z/nZ of residues (mod n) as a dynamical system, whose cycles relatively prime to n all have a common period T (n) and whose orbits consist each of T (n) elements, forming a geometrical progression or residues. The paper provides many new facts on the arithmetical properties of these periods and orbits (generalizing the Fermat’s small ...

We study the local complete synchronization of discrete-time dynamical networks with time-varying couplings. Our conditions for the temporal variation of the couplings are rather general and include both variations in the network structure and in the reaction dynamics; the reactions could, for example, be driven by a random dynamical system. A basic tool is the concept of Hajnal diameter which ...

This paper explores the visualization of two-dimensional stable and unstable manifolds of the origin (a saddle point) in a four-dimensional Hamiltonian system arising from control theory. The manifolds are computed using an algorithm that finds sets of points that lie at the same geodesic distance from the origin. By coloring the manifolds according to this geodesic distance, one can gain insig...

We argue that classical non-Abelian gauge theory provides an example of 't Hooft's scenario, in which quantum mechanics is generated at large distances in a classical dynamical system. Using the known properties of thermal field theories, we show how the transformation from classical to quantum dynamics emerges. Planck's constant ¯ h is defined in terms of the quantities of the underlying class...

Upper tropospheric humidity plays an important role in the formation and maintenance of tropical cirrus clouds. Deep convection is crucial for the transport of water vapor from the boundary layer to the upper troposphere and is responsible for the formation of anvil cirrus that can spread horizontally over considerable distances and persist for several hours. In addition, recent studies have li...

Direct imaging is a technique commonly used in the study of particle, bubble, and droplet size distribution in a dynamic system. Objects such as particles, bubbles, and droplets can be present at various distances from the imaging device when images are captured. Hence, the location of the object will need to be known in order to determine the actual size of an individual object. However, the l...

Localization arises repeatedly in many location-aware applications such as navigation, autonomous robotic movement, and asset tracking. Analytical localization methods include triangulation and trilateration. Triangulation uses angles, distances, and trigonometric relationships to locate an object. Trilateration, on the other hand, uses only distance measurements to identify the position of the...

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems are giv...