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When multiple stable responses are possible the domains of attraction are determined.
It is demonstrated that the coupled system of flow-cylinder-NES behaves resonant interactions, showing periodic, aperiodic, and multiple stable responses which depend on the values of the NES parameters.
In addition, it is found that the occurrence of multiple stable responses can enhance the nonlinear energy pumping effect, resulting in the increment of transferring energy from the flow via the cylinder to the NES, which is related to the essential nonlinearity of the sink stiffness.
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Instead the bistability is reflected in the fact that (depending on signal ranges) it is possible to have multiple stable spatially graded responses, which may be seen as spatial analogues of the temporal behaviour of the module.
The difference between the structural responses leading exhibited by the multiple stable shapes of the designed composites are numerically investigated.
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].
Multi-stability of a dynamic system consists of the ability to express, for a given set of parameters, multiple stable states and to switch between these states in response to some external transient input.
Among the pathological responses obtained for the CSTR example are multiple stable forced states, subharmonic oscillations, and almost periodic outputs.
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.
In an approach involving spatial data, Hirota et al. (2011) investigated forest response to climate stressors by analyzing remotely sensed imagery to demonstrate evidence for multiple stable tree distribution states and sharp transitions related to precipitation amounts.
In this investigation, system (2.3) has multiple stable equilibrium points.
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