Growth Rates under Interval Uncertainty

For many real-life systems ranging from financial to populationrelated to medical, dynamics is described by a system of linear equations. For such systems, the growth rate λ can be determined as the largest eigenvalue of the corresponding matrix aij . In many practical situations, we only know the components of the matrix aij with interval (or fuzzy) uncertainty. In such situations, it is desirable to find the range of possible values of λ. In this paper, we propose an efficient algorithm for computing λ for a practically important case when all the components aij of the matrix are non-negative. 1 Growth Rates: A Linear Approximation to the Description of a General System General description. In general, the state of a real-life complex system can be described by listing the current values of its parameters x1, . . . , xn. – For continuous-time systems, their dynamic can be described as ẋi = fi(x1, . . . , xn) for some functions f1, . . . , fn. – For discrete-time systems, their dynamic can be described as xi(t + 1) = fi(x1(t), . . . , xn(t)) for some functions f1, . . . , fn. Linearized description. The dependencies fi(x1, . . . , xn) are usually smooth, so within a reasonable range of values xi, we can approximate each of these functions by a linear expression: fi(x1, . . . , xn) = bi + n ∑