The authors regret to inform the readers that the original publication1 needs to be amended as follows (the modifications with respect to the original text are highlighted in blue). • In Section 2.1 (The considered class of systems), item (2) should read: For λ ∈ I \{λ0}, Gλ is obtained from Gλ0 via the addition of the stochastic stationary noise term ηλ multiplied by the smooth function g(x) to the right hand side of the ODE in (2). Hence, the state of Gλ at time t > 0 is a random variable, defined on a suitable probability space with probability ℙλ that is induced by the stochastic noise ηλ. • In Section 2.1, the paragraph before Example 1 should read: Let A be a closed attractor of Gλ0 and B(A) = {χ ∈ U : limt→∞ dist(x(t; χ, 0), A) = 0} the associated basin of attraction, where x(t; χ, 0) denotes the trajectory of the nominal system Gλ0, with ηλ0 ≡ 0, starting from initial condition χ. We assume that g(x) = 0 for all x ∈ A. Given λ ∈ I \ {λ0}, a natural question to ask is whether the attractor-basin pair (A, B(A)) preserves its properties for some/all the systems in F. Before proceeding, we examine two examples from the biological literature. • In Section 2.1, in all the equations related to the considered examples, the noise intensity λ should be also multiplied by a smooth function of the state that is zero on the considered attractor. For instance, Eq. (5) should read: (Formula presented). • At the beginning of Section 3 (Numerical Examples) it should be clarified that, for all the considered examples, we choose the smooth function g(x) as a cutoff function satisfying g(x) = 0 for x ∈ A + φB(0, 1) and g(x) = 1 for x ∉ A + 2φB(0, 1), where φ > 0 is small and B(0, 1) is the unit ball around zero. The authors would like to apologise for any inconvenience caused.
Corrigendum to: Bridging Robustness and Resilience for Dynamical Systems in Nature (IFAC-PapersOnLine (2024) 58:17 (43-48) PII: S2405896324018664 DOI: 10.1016/j.ifacol.2024.10.111) / Proverbio, D.; Katz, R.; Giordano, G.. - In: IFAC PAPERSONLINE. - ISSN 2405-8971. - 58:17(2024), pp. 445-445. ( 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024 Cambridge, UK 19-23 August 2024) [10.1016/j.ifacol.2025.07.111].
Corrigendum to: Bridging Robustness and Resilience for Dynamical Systems in Nature (IFAC-PapersOnLine (2024) 58:17 (43-48) PII: S2405896324018664 DOI: 10.1016/j.ifacol.2024.10.111)
Proverbio D.;Giordano G.
2024-01-01
Abstract
The authors regret to inform the readers that the original publication1 needs to be amended as follows (the modifications with respect to the original text are highlighted in blue). • In Section 2.1 (The considered class of systems), item (2) should read: For λ ∈ I \{λ0}, Gλ is obtained from Gλ0 via the addition of the stochastic stationary noise term ηλ multiplied by the smooth function g(x) to the right hand side of the ODE in (2). Hence, the state of Gλ at time t > 0 is a random variable, defined on a suitable probability space with probability ℙλ that is induced by the stochastic noise ηλ. • In Section 2.1, the paragraph before Example 1 should read: Let A be a closed attractor of Gλ0 and B(A) = {χ ∈ U : limt→∞ dist(x(t; χ, 0), A) = 0} the associated basin of attraction, where x(t; χ, 0) denotes the trajectory of the nominal system Gλ0, with ηλ0 ≡ 0, starting from initial condition χ. We assume that g(x) = 0 for all x ∈ A. Given λ ∈ I \ {λ0}, a natural question to ask is whether the attractor-basin pair (A, B(A)) preserves its properties for some/all the systems in F. Before proceeding, we examine two examples from the biological literature. • In Section 2.1, in all the equations related to the considered examples, the noise intensity λ should be also multiplied by a smooth function of the state that is zero on the considered attractor. For instance, Eq. (5) should read: (Formula presented). • At the beginning of Section 3 (Numerical Examples) it should be clarified that, for all the considered examples, we choose the smooth function g(x) as a cutoff function satisfying g(x) = 0 for x ∈ A + φB(0, 1) and g(x) = 1 for x ∉ A + 2φB(0, 1), where φ > 0 is small and B(0, 1) is the unit ball around zero. The authors would like to apologise for any inconvenience caused.| File | Dimensione | Formato | |
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