Suchergebnisse

[EN] We combine the stochastic perturbation method with the maximum entropy principle to construct approximations of the first probability density function of the steady-state solution of a class of nonlinear oscillators subject to small perturbations in the nonlinear term and driven by a stochastic excitation. The nonlinearity depends both upon position and velocity, and the excitation is given by a stationary Gaussian stochastic process with certain additional properties. Furthermore, we approximate higher-order moments, the variance, and the correlation functions of the solution. The theoretical findings are illustrated via some numerical experiments that confirm that our approximations are reliable. ; This work has been supported by the Spanish Ministerio de Economía, Industria y Competitividad (MINECO), the Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017¿89664¿P. Elena López-Navarro has been supported by the European Union through the Operational Program of the [European Regional Development Fund (ERDF)/European Social Fund (ESF)] of the Valencian Community 2014-2020 (GJIDI/2018/A/010) ; Cortés, J.; López-Navarro, E.; Romero, J.; Roselló, M. (2021). Approximating the Density of Random Differential Equations with Weak Nonlinearities via Perturbation Techniques. Mathematics. 9(3):1-17. https://doi.org/10.3390/math9030204 ; S ; 1 ; 17 ; 9 ; 3

[EN] We provide a full stochastic description, via the first probability density function, of the solution of linear-quadratic logistic-type differential equation whose parameters involve both continuous and discrete random variables with arbitrary distributions. For the sake of generality, the initial condition is assumed to be a random variable too. We use the Dirac delta function to unify the treatment of hybrid (discrete-continuous) uncertainty. Under general hypotheses, we also compute the density of time until a certain value (usually representing the population) of the linear-quadratic logistic model is reached. The theoretical results are illustrated by means of several examples, including an application to modelling the number of users of Spotify using real data. We apply the Principle Maximum Entropy to assign plausible distributions to model parameters ; This work has been supported by the Spanish Ministerio de Economa, Industria y Competitividad (MINECO) , the Agencia Estatal de Investigaci on (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM201789664P. Computations have been carried thanks to the collaboration of Raul San Julian Garces and Elena Lopez Navarro granted by European Union through the Operational Program of the European Regional Development Fund (ERDF) /European Social Fund (ESF) of the Valencian Community 2014-2020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010, respectively ; Burgos-Simon, C.; Cortés, J.; López-Navarro, E.; Villanueva Micó, RJ. (2021). Probabilistic analysis of linear-quadratic logistic-type models with hybrid uncertainties via probability density functions. AIMS Mathematics. 6(5):4938-4957. https://doi.org/10.3934/math.2021290 ; S ; 4938 ; 4957 ; 6 ; 5 ; R. Goebel, R. G. Sanfelice, A. R. Teel, i>Hybrid Dynamical Systems: Modeling, Stability, and Robustness /i>, Princeton University Press, 2012. ; J. Lunze, F. Lamnabhi-Lagarrigue, i>Handbook of Hybrid Systems Control: Theory, Tools, Applications /i>, ser. Nonlinear Systems and Complexity, ...