Sentence examples for system an exponential from inspiring English sources

In the investigation of absolute stability of the control systems with delay, we will use Lyapunov-Krasovskii functionals which contain, in addition to the quadratic form and the integral of the nonlinear component of the considered system, an exponential multiplier, i.e., V [ x ( t ), σ ( t ) ] = h x 2 ( t ) + g ∫ t − τ t e − ξ ( t − s ) x 2 ( s ) d s + β ∫ 0 σ ( t ) f ( s ) d s, (4).

This means that both the time between user arrivals to the system and the service time of the system follow an exponential distribution with means λ and μ respectively, with m servers with an FCFS scheduling policy.

By constructing an appropriate Lyapunov Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system.

Thus, since a system involves an exponential divergence of nearby trajectories only if it is a K-system, it is concluded that (merely) ergodic and mixing systems are not chaotic whereas K- and B-systems are.

The model is described by a continuous time four-dimensional autonomous system with an exponential nonlinearity.

We prove a result ensuring the existence of an almost automorphic solution for both equations, assuming that the associated homogeneous equation of this system admits an exponential dichotomy.

In this work we take into account this slip and prove that we can stabilize the system in an exponential manner using boundary controls.

In this respect, Amster et al. [6] studied boundary value problems for dynamic systems and proved the existence of solutions via topological degree theory; Lizama and Mesquita [7] considered nonautonomous dynamic equations and proved the existence of almost automorphic solutions by assuming that the associated homogeneous equation of the system admits an exponential dichotomy.

First let us consider the system with an exponential activation function such that d A d t = ( 1 1 + e − ( ( w / N ) A + h ) − 1 2 ) ( N − A ) − α A. This function saturates and so is somewhat more realistic than the linear function considered previously.

We began by investigating how organisms with forward or reverse polymerases would behave in the model system during an exponential growth phase in the absence of competitive pressure.

From the view point of the Boltzmann formula, Dragulescu and Yakovenko 19 suggested that any conserved quantity in a big statistical system has an exponential probability distribution in equilibrium.