Sentence examples for many dynamical systems from inspiring English sources

Time delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, economic models [1, 2], biological systems [3], and in competition in population dynamics [4].

However, many dynamical systems possess an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process.

Indeed, many dynamical systems have an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process.

To describe the anomalous inner structure of economic and financial models, many dynamical systems are proposed to model the relations of macroeconomic variables.

Many dynamical systems depend not only on present and past states but also involve derivatives with delays as well as the function itself.

On the other hand, many dynamical systems depend not only on present and past states, but also involve derivatives with delays.

Impulsive fractional differential equations are used to describe many practical dynamical systems in many evolutionary processes models.

In particular, impulsive fractional evolution equations are used to describe many practical dynamical systems in many evolutionary processes models.

Fractional differential equations are well known to describe many sophisticated dynamical systems in physics, fluid dynamics, praxiology, viscoelasticity and engineering.

Nonlinear partial differential equations (NLPDEs) are widely used as models to describe many important dynamical systems in various fields of science, particularly in fluid mechanics, solid state physics, plasma physics and nonlinear optics.

Thus, stochastic differential equations have attracted great interest due to their extensive applications in describing many sophisticated dynamical systems in physical, biological, medical, and social sciences; see [1, 35 42] and the references therein for details.