A review on phase plane and non-linear system of differential equations with application
Keywords:Phase portrait, Phase trajectory, Closed orbit, Separatrix, Eigenvalues, Linearization
In this paper we review on nonlinear phenomena and properties, particularly those with physical relevance. Often, mathematical models of real-world phenomena are formulated in terms of systems of nonlinear differential equations, which may be difficult to solve explicitly. Finding a solution to a differential equation may not be so important if that solution never appears in the physical model represented by the system, or is only realized in exceptional circumstances. Thus, equilibrium solutions, which correspond to configurations in which the physical system does not move, only occur in everyday situations if they are stable. An unstable equilibrium will not appear in practice, since slight perturbations in the system or its physical surroundings will immediately dislodge the system far away from equilibrium. We take a qualitative approach to the analysis of solutions to nonlinear systems by making phase portraits and using stability analysis.
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Copyright (c) 2021 Asnake Tadese Abtew,Tesfaye Tefra Mamo
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