Study of nonhomogeneous linear second‐order discrete dynamical systems with uncertainties: Solution and stability with applications

We study, from a probabilistic standpoint, a full randomization of nonhomogeneous second‐order linear difference equations assuming that its data (initial conditions, coefficients, and forcing term) are random variables. Our analysis consists of computing the so‐called first probability density func...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-03, Vol.47 (5), p.3345-3360
Main Authors: Cortés, Juan‐Carlos, Navarro‐Quiles, Ana, Sferle, Sorina‐Madalina
Format: Article
Language:English
Subjects:
Difference equations
Dynamic stability
Initial conditions
Probability density functions
Random variables
Stability analysis
Statistical analysis
Stochastic processes
Uncertainty
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Summary:We study, from a probabilistic standpoint, a full randomization of nonhomogeneous second‐order linear difference equations assuming that its data (initial conditions, coefficients, and forcing term) are random variables. Our analysis consists of computing the so‐called first probability density function of the solution, which is a stochastic process, and then analyzing the stability of the solution assuming that all data have an arbitrary joint probability density function. To achieve these goals, we take extensive advantage of the so‐called random variable transformation technique. The theoretical results extend their deterministic counterpart, and then, they have many applications in real‐world problems where uncertainty plays a key role. Our findings are first illustrated by means of several numerical examples, where different simulations are carried out, and, second, by means of a model belonging to biomathematics.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.8210