the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

Nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. The study of dynamical properties of such equations is of great importance in many areas. The autonomous difference equat...

Clean energy harvesting and usage has gained considerable attention in the last few decades. While the horizontal axis wind turbines have been used extensively, they have certain defects and functional limitations. In the present paper, a novel oscillatory wind turbine is proposed. The conceptual design of the new turbine together with its configuration is explained. Dynamical equations of the ...

A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. ‘Microscopic’ assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations. That means, the approximate mean value equations of these equations are the game dynamical equations of evolutionary game theory. The stochastic version of the...

Usually mathematicians use Hodgkin-Huxley model or FitzHug-Nagumo model to simulate action potentials of skeletal muscle fibers. These models are electrically excitable, but skeletal muscle fibers are stimulated chemically. To investigate skeletal muscle fibers we use a model with six ordinary differential equations. This dynamical system is sensitive to initial value of some variables so it is...