| Popis: |
Consider the augmented differential delay equation initial value problem (with τ ≡ 1) $$\displaystyle \begin {aligned}{} &x'(t) = \begin {cases} \mathcal {G}\big ( x(t) \big ) & t \in [0,1) \\ \mathcal {F}\big ( x(t), x(t-1) \big ) & t \geq 1 \end {cases} \\ &x(0) = x_0, \end {aligned} $$ with \(x(t) \in \mathbb {R}\), and suppose that an ensemble of initial values x0 is specified with density f0. We would like to derive an evolution equation for the density f(x, t) of the corresponding ensemble of solutions x(t). |
