Sentence examples for behavior of the dynamical from inspiring English sources

It is designed so that it preserves positivity of solutions and the local behavior of the dynamical system near equilibria.

The course uses examples from biology as an integrating theme, principles from physics and mathematics to reduce complex problems to simpler forms, and computer simulation to allow students to develop their intuition about the behavior of the dynamical systems that control the physical and biological universe.

The phase plots show the behavior of the dynamical system in modes 1 and 3.

That is, the change in the initial condition is not such that it changes the qualitative behavior of the dynamical system for (0< t ll 1)—only the quantitative properties are dramatically altered.

As explained in detail in many works in the field of fuzzy differential equations, uncertainty has to be considered in the formulation of a mathematical model for a better adequacy, due to the imprecision inherent to the information available or the behavior of the dynamical system itself (see, for instance, [3]).

Different from the classical Lyapunov stability concept, finite-time stability is defined as the behavior of the dynamical systems that can be tracked over a fixed finite-time interval, that is, the system state does not exceed a certain bound during a fixed finite-time interval.

However, if we want to investigate the model behavior for the entire space, we need to decompose it into regions characterized by asymptotically different behaviors of the dynamical systems.

In general, in a dynamical system, if a parameter is allowed to vary, then the behavior of the whole dynamical system may change.

To get a feeling of what is going on, the dynamical behaviors of the systems (5.2) and (5.3) can be seen Figures 1 and 2. Figure 1 The dynamical behavior of the system ( 5.2 ). Figure 2 The dynamical behavior of the system ( 5.3 ).

We give theoretical results for the behavior of the solution to the dynamical system in Eq. (8).

It is not surprising that one witnesses a surge of research interest in the analysis of the dynamical behavior of complex dynamical networks.