Basins of Attraction and Stability of Nonlinear Systems’ Equilibrium Points
The system of differential and operator equations is considered. This system is assumed to enjoy an equilibrium point. The Cauchy problem with the initial condition with respect to one of the desired functions is formulated. The second function controls the corresponding nonlinear dynamic process. T...
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| Veröffentlicht in: | Differential equations and dynamical systems 2023-04, Vol.31 (2), p.289-300 |
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| container_title | Differential equations and dynamical systems |
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| creator | Sidorov, Nikolay Sidorov, Denis Li, Yong |
| description | The system of differential and operator equations is considered. This system is assumed to enjoy an equilibrium point. The Cauchy problem with the initial condition with respect to one of the desired functions is formulated. The second function controls the corresponding nonlinear dynamic process. The sufficient conditions of the global classical solution’s existence and stabilisation at infinity to the equilibrium point are formulated in the main theorem. Solution can be constructed by the method of successive approximations. If the conditions of the main theorem are not satisfied, then several solutions may exist. Some solutions can blow-up in a finite time, while others stabilise to an equilibrium point. The special case of considered systems of differential-operator equations are nonlinear systems of differential-algebraic equations which model various nonlinear phenomena in power systems, chemical processes and many other processes. |
| doi_str_mv | 10.1007/s12591-019-00511-w |
| format | Article |
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| subjects | Cauchy problems Chemical reactions Computer Science Differential equations Dynamical systems Engineering Mathematics Mathematics and Statistics Nonlinear dynamics Nonlinear phenomena Nonlinear systems Operators (mathematics) Original Research Theorems |
| title | Basins of Attraction and Stability of Nonlinear Systems’ Equilibrium Points |
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