Stability-analysis-of-linearised-models-graphical-analysis

The codes will help you to explore the impact of parametric signs on the dynamics of linearised models around equilibria.

Consider the systems du/dt = au+bv; dv/dt = cu+dv; (1) we linearise nonlinear models of epidemiological problems to explore the dynamics of the systems more swiftly. The analytic solutions and six cases emerging from system (1) are discussed graphically. The red dot is the initial condition. Arrows provide information about the direction of the trajectory. ▶ Case (i): Asymptotically stable or unstable, depending on the signs of λ and μ. ▶ Case (ii): Asymptotically stable or unstable based on the sign of λ. ▶ Case (iii): Asymptotically stable or unstable, with potential for maximum/minimum trajectories. ▶ Case (iv): Saddle point, inherently unstable. ▶ Case (v): Center, neutral stability with circular orbits. ▶ Case (vi): Asymptotically stable or unstable, with spiraling orbits. Note that in the cases above, we had a = lambda; b = 0 in most of the cases, c = 0 in all cases and d = mu in many cases. I hope you will edit the values for these parameters and explore the dynamics and will try to map on existing limit cycles and spirals in the real world such as chaos and climate change challenges, galaxies and biophysics.