Non-linear dose response relationships pose statistical challenges for their discovery. Even when an initial linear approximation is followed by other approaches, the results may be misleading and, possibly, preclude altogether the discovery of the nonlinear relationship under investigation. We review a variety of straightforward statistical approaches for detecting nonlinear relationships and ...

Children's ability to place fractions on a number line strongly correlates with math achievement. But does the number line play a causal role in fraction learning or does it simply index more advanced fraction knowledge? The number line may be a particularly effective representation for fraction learning because its properties align with the desired mental representation and take advantage of p...

in purpose of this paper is to discuss the occurance of bifurcation and chaos in nonlinear systems in general, and the pearl-reed model whi.ch has been used for representing the lynamical behavior of the petroleum resources in particular. based on this investigation, it is shown that the observed tluctuations in the petroleum market can be erplained by its interral dynamics and the increase in ...

Risk factors are generally defined and assigned to road networks, as constant measures in hazmat routing problems. In fact, they may be dynamic variables depending on traffic volume, weather and road condition, and drivers' behavior. In this research work, risk factors are defined as dynamic variables using the concept of chaos theory. The largest Lyapunov exponent is utilized to determine the ...

The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in the paper. In order to suppress the irregular chaotic motion, an optimal backstepping controller is designed. The backstepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the syste...

The discovery of fifth nonlinear region of operation i.e. quasi–chaos is confirmed in this paper after its recently reported two observations in loss and pumpmodulated Erbium doped fiber ring lasers.Quasi-chaos is apparently chaos but its time and physical phase space trajectories actually converge instead of diverging, even for widely separated initial conditions once the system numerical mode...

In recent years, encryption technology has been developed rapidly the chaos based cryptographic algorithms. Chaos owns certain critical properties such as sensitive dependence on initial condition, random-like behavior, and continuous broadband power spectrum, which match the confusion, diffusion, and key sensitivity requirements for cryptography. Chaos based cryptographic offer sundry features...

Control of chaos in the single-mode optically pumped far-infrared NH3 laser is experimentally demonstrated using continuous time-delay control. Both the Lorenz spiral chaos and the detuned period-doubling chaos exhibited by the laser have been controlled. While the laser is in the Lorenz spiral chaos regime the chaos has been controlled both such that the laser output is cw, with corrections of...