Nullclines, Equilibria, and Phase Portrait for a Nonlinear System of Differential Equations

Consider the nonlinear system x' = y - x^2 + a, y' = y + x^2 - a. When a is positive, nullclines are graphed, equilibrium points are solved for, and the phase portrait is sketched in the phase plane. The Jacobian matrix is also found to linearize near the equilibria. https://amzn.to/35Wxabr. (Differential Equations, 4th Edition (by Blanchard, Devaney, and Hall)). Amazon Prime Student 6-Month Trial: https://amzn.to/3iUKwdP. #nullclines #PhasePortrait #PhasePlane Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinneymath?sub_confirmation=1 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter: https://twitter.com/billkinneymath 🔴 Follow me on Instagram: https://www.instagram.com/billkinneymath/ 🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.