Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. However, I cannot visualize the isolated periodic trajectories.Wolfram Data Framework Semantic framework for real-world data. How may I construct the phase portrait of this system without using StreamPlot? (Attached below, you may see my notebook, in which a phase portrait is made by employing the StreamPlot command. It is already well-known that the dynamical system has four limit cycles. The system has 3 equilibrium points: in (0 0) there is a saddle, in (0.08 0) there is a centre, and in (-0.08 0) there is also a centre. With that said, suppose that we have the following nonlinear dynamical system Therefore, to plot a phase portrait for a first order differential equation d y / d x f ( x, y), a user needs to set 1 for the first coordinate and f for the second one, so making the vector input ( 1, f ( x, y)). Owing to the fact that phase portrait and phase spaces are quite interesting topics on nonlinear dynamics, I think that these questions, and their possible answers, may be of great interest to those that subscribe to the Mathematica forum. However, these did not help me with the questions to be presented here. In addition, I have read Mathematica's documentation. It should be remarked that I have also searched and read previous discussions from Mathematica Forum. I have elementary questions about the construction of phase portraits and limit cycles using Mathematica.
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