Heteroclinic orbit

In mathematics, in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins two different equilibrium points. If the equilibrium points at the start and end of the orbit are the same, the orbit is a homoclinic orbit. In mathematics, in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins two different equilibrium points. If the equilibrium points at the start and end of the orbit are the same, the orbit is a homoclinic orbit. Consider the continuous dynamical system described by the ODE Suppose there are equilibria at x = x 0 {displaystyle x=x_{0}} and x = x 1 {displaystyle x=x_{1}} , then a solution ϕ ( t ) {displaystyle phi (t)} is a heteroclinic orbit from x 0 {displaystyle x_{0}} to x 1 {displaystyle x_{1}} if