6 problems

Consider the stochastic version of the Brusselator with the noisy perturbation formulated in the cited stochastic model. In the deterministic Brusselator with large bifurcation par…

Let the Brusselator be subjected to a noisy term representing a stochastic variation of its bifurcation parameter. Parametric-noise destruction conjecture. Parametric noise destroy…

Consider the stochastic Brusselator system with noise intensity $\sigma>0$. A random equilibrium is a random state invariant under the cocycle dynamics, namely a measurable point…

Consider the stochastic Brusselator with parameters $a$, $b$, and $\sigma$, and let $\varphi^t_\omega$ denote the cocycle map generated by a common noise realization $\omega$. Two…

Let $a,b,\sigma>0$ and let $A(\omega)$ be the random equilibrium of the stochastic Brusselator, satisfying … almost surely. Newman's conjecture. The top Lyapunov exponent is negati…

Let $a,b,\sigma>0$ and consider the stochastic Brusselator as a smooth random dynamical system $(\theta,\varphi)$ on $\mathbb{R}_+^2$, with stationary distribution $\rho$, invarian…