Study of stability of a stochastic model of the ``dangling spider'' problem. III (Q5942121)

The stochastic ``dangling spider'' model is studied which is defined by the stochastic system of functional-differential equations \[ \begin{aligned} dx(t) &= y(t) dt,\\ dy(t) &= \Biggl[F(x(t))+ \int^\infty_0 k(s) g(x^t(s)- x(t))\Biggr] dt+ \sigma(X^t) dw(t)+ \int_U x(t) c(u)\widetilde v(du, dt),\end{aligned} \] where \(X(t)= (x(t), y(t))^T\); \(\{w(t)\}\) is the Wiener process; \(\widetilde v(du,dt)\) is the centered Poisson measure, and \(w(t)\) and \(\widetilde v(du,dt)\) are independent of one another. The authors consider the problem of the stability of this model.