Non-linear behaviors of a single neuron described by Fitzhugh-Nagumo (FHN) neuron model, with external electromagnetic radiation considered, is investigated. It is discovered that with external electromagnetic radiation in form of a cosine function, the mode selection of membrane potential occurs among periodic, quasi-periodic, and chaotic motions as increasing the frequency of external transme...

mas·hyy saturated soil liquefaction during earthquakes, shnakhthshdhyy phenomenon that many researchers in the past three decades has attracted. more research on the liquefaction of saturated soils has focused mas·hyy the natural soils are rarely composed of clean sands, and mixed with clay or silt soils, which is why the study has important ghyrkhmyry and paste. despite numerous studies on the...

Chaos is an aperiodic long-term behavior in a deterministic system that exhibits sensitively dependent on initial conditions. There are three keywords in this definition, i.e. “aperiodic long-term behavior”, “deterministic” and “sensitive dependence on initial conditions”. “Aperiodic long-term behavior” means that the system’s trajectory in phase space does not settle down to any fixed points, ...

The unix rusage statistics are well known to be highly inaccurate measurements of CPU utilization. We have observed errors in real applications as large as 80%, and we show how to construct an adversary process that can use an arbitrary amount of the CPU without being charged. We demonstrate that these inaccuracies result from aliasing effects between the periodic system clock and periodic proc...

The crustacean pyloric Central Pattern Generator (CPG) is a nervous circuit that endogenously provides periodic motor patterns. Even after about 40 years of intensive studies, the rhythm genesis is still not rigorously understood in this CPG, mainly because it is made of neurons with irregular intrinsic activity. Using mathematical models we addressed the question of using a network of irregula...

We respond to Sornette and Johansen’s criticisms of our findings regarding log-periodic precursors to financial crashes. Included in this paper are discussions of the Sornette-Johansen theoretical paradigm, traditional methods of identifying log-periodic precursors, the behavior of the first differences of a log-periodic price series, and the distribution of drawdowns for a securities price.

We report numerical and experimental results indicating successful stabilization of unstable steady states and periodic orbits in an electrochemical system. Applying a continuous delayed-feedback technique not only periodic and chaotic oscillations are suppressed via stabilization of steady-state solutions but also the chaotic dynamics can be converted to periodic behavior. In all cases the fee...

In this paper, by the weighted ergodic function based on the measure theory, we study the pseudo asymptotic behavior of mild solution for semilinear fractional integro-differential equations. The existence, unique of -pseudo anti-periodic ( -pseudo periodic, -pseudo almost periodic, -pseudo almost automorphic) solution are investigated. Moreover, an application to fractional partial differentia...

We prove that the seasonally-forced SIR model with a T -periodic forcing has a periodic solution with period T whenever the basic reproductive number R0 > 1. The proof uses the Leray-Schauder degree theory. We also describe some numerical results in which we compute the T -periodic solution, where in order to obtain the T -periodic solution when the behavior of the system is subharmonic or chao...