Sentence examples for multiple stable solutions from inspiring English sources
It is known that in some cases the method can yield multiple stable solutions for the mean value and the standard deviation of the system response.
Mixed colors are used to indicate the co-existence of multiple stable solutions, but for clarity, we also show the stability regions for each type of solution separately in Figure 8. Fig. 7 Bifurcations in two parameters.
The ability to observe such systems in distinct physiological forms within a unique environment was found to be consistent with the existence of multiple stable solutions of the representative balance equations.
The model exhibits multiple stable solutions and periodic solutions which have been seen experimentally in monoliths [1], [2] and single-channel models [3] but have not been explored theoretically in multi-channel models.
For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches.
Multiple stable chaotic solutions corresponding to distinct but extremely close initial conditions are revealed.
These multiple stable periodic solutions differ in amplitude and period and have their own basins of attraction.
Recently, HTLV-I model with time delays in the CTL response leading to the coexistence of multiple stable periodic solutions has been studied in [17].
Furthermore, the noise fluctuations of the system induce early transition to chaos for a system undergoing a sequence of period doubling bifurcations to chaos, and destabilize first the solution with "weaker protection" for a system having multiple stable steady state solutions.
This is particularly useful in beam buckling problems where multiple stable and unstable solutions exist.
The temperature versus strain rate response curves exhibit multiple branches of stable solutions, implying a possibility of hysteresis behavior in a coupled homogeneous heterogeneous reactor.
