Use ordinary differential equations.
See https://www.mathworks.com/help/matlab/ref/ode45.html for basic usage of ODE45 and https://www.mathworks.com/matlabcentral/answers/161511-solving-complex-coupled-differential-equations for a complicated example.
Hi Kajal Maji,
With the vector field plot, you can visualize the trajectories of x and y. There are two equilibrium points:
P1(0, 0) -- a saddle point (unstable)
P2(2, 1/3) -- a center (stable)
They are found by solving:
x − 3*x*y = 0;
0.25*x*y − 0.5*y = 0;
For "nonlinear coupled differential equations", try the FortranCalculus (FC) language that got its start by NASA's Apollo Space program.
FC-Compiler™ application is a (free) Calculus-level Compiler that simplifies Tweaking parameters in ones math model. FC solves Algebraic through Ordinary Differential Equations Equations; Laplace transforms; etc. FC is based on Automatic Differentiation that simplifies computer code to an absolute minimum; i.e., a mathematical model, constraints, and the objective (function) definition.
Most math Modeling, Simulations, & Optimizations can be easily solved with a Calculus-level language/compiler. A half-hour per problem should be enough time to code and execute most math problems. Solves Algebraic Equations through Ordinary Differential Equations, for more visit http://fortrancalculus.info/apps/fc-compiler.html . Equations may be implicit, non-linear, Boundary Value Problems (BVP), Initial Value Problems (IVP), etc. Download, install, & execute some demo problems. Simple and its Freeware! (PDE solvers are in the works!)
- Badges
- Science topic