Sentence examples for by linear dynamic equations from inspiring English sources

They are described by linear dynamic equations subject to linear inequalities involving real and integer variables.

For the model, we have given some sufficient conditions ensuring the existence and global exponential stability of almost periodic solutions by using the exponential dichotomy of linear dynamic equations on time scales, Banach's fixed point theorem and the theory of calculus on time scales.

By utilizing the exponential dichotomy of linear dynamic equations on time scales, Banach's fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solutions for this class of neural networks.

Remark 2.12 Choi et al. [14], Theorem 2.16] studied h-stability for linear dynamic equations on time scales by using the unified time scale quadratic Lyapunov functions.

By the way, (4) is a system of ordinary linear dynamic equations of first order.

We examine the conditions of asymptotic stability of second-order linear dynamic equations on time scales.

The oscillation properties of second-order linear dynamic equations are studied in [25] and the oscillation and non-oscillation behavior of second-order half-linear dynamic equations is investigated in [26 28].

These lemmas are based on the linear dynamic equation: (2.1).

Finally, we give an illustrative example for a nonregressive homogeneous first-order linear dynamic equation and we investigate its stability.

The non-linear dynamic equations of the rotor are obtained.

Hassan [7] considered the second-order half-linear dynamic equations on time scales (31).