We present an overview of mechanisms responsible for simple or complex oscillatory behavior in metabolic and genetic control networks. Besides simple periodic behavior corresponding to the evolution toward a limit cycle we consider complex modes of oscillatory behavior such as complex periodic oscillations of the bursting type and chaos. Multiple attractors are also discussed, e.g., the coexist...

For $C^{1}$-smooth strongly monotone discrete-time dynamical systems, it is shown that “convergence to linearly stable cycles” a prevalent asymptotic behavior in the measure-theoretic sense. The results are then applied several classes of time-periodic parabolic equations and obtain prevalence convergence periodic solutions.

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

The objective of this study was to model seasonal behavior of broiler price in Iran that can be used to forecast the monthly broiler prices. In this context, the periodic autoregressive (PAR), the seasonal integrated models, and the Box-Jenkins (SARIMA) models were used as the primary nominates for the forecasting model. It was shown that the PAR (q) model could not be considered as an appropri...

We study the effects of sinusoidally modulating the current injected into a model sensory neuron from the weakly electric fish Apteronotus leptorhynchus. This neuron's behavior is known to switch from quiescence to periodic firing to bursting as the injected current is increased. The bifurcation separating periodic from bursting behavior is a saddle-node bifurcation of periodic orbits, and it h...

The interaction of a system with quasi-periodic autonomous dynamics and chaotic (Rossler system) is considered. behavior Lyapunov exponents studied to identify possible types dynamics: chaos additional zero exponents, three-frequency two-frequency regimes, periodic oscillations the mode oscillation death. Keywords: oscillations, dynamical chaos, Rossler system, exponents.

this paper studies the generalized version of thezakharov-kuznetsov benjamin-bona-mahoney equation. the functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. there are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. the results of this pape...

a new dynamic friction model for modeling of elliptical vibration assisted turning (evat) was developed in this research. the periodic change of the friction force direction is known to be one of the most important causes of this phenomenon. in modeling of machining processes (including the evat process), static coulomb friction model was employed by most of the researchers. because of the peri...

free surface sloshing of liquid in a rectangular tank induced by lateral excitation has been studied numericallyand experimentally in this paper. the numerical simulation is carried out based on the volume of fluid (vof) method that provides free surface extraction in such problem. a tank with transparent walls is used to free surface tracking in experimental study while the movement amplitude ...