We often encounter nonlinear dynamical systems that behave unpredictably, such as the earth's climate and the stock market. To analyze them, measurements taken over time are used to reconstruct the ...
Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...
1 Civil, Environmental and Architectural Engineering, University of Colorado Boulder, Boulder, CO, USA, 2 Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado ...
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Can deep learning techniques predict sudden state transitions in nonlinear dynamical systems?
Nonlinear dynamical systems are systems that can undergo sudden shifts not due to changes in their state or stability, but in response to the rate at which external conditions or parameters change.
Imagine standing on top of a mountain. From this vantage point, we can see picturesque valleys and majestic ridges below, and streams wind their way downhill. If a drop of rain falls somewhere on this ...
Mathematical models about how mass moves in natural systems are used in various scientific fields such as to understand the global carbon and water cycles, or predicting the spread of contaminants or ...
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