Most of the complex systems cannot be properly described without considering the random sources that often affect their dynamics. The inclusion of randomness in dealing with complex systems is a relatively new area where Mathematics, Probability and Statistics and Computation are masterly met. This fact makes the difference since there are very few contexts where distinctive approaches of these important realms can act all together to sort out relevant problems. Indeed, nonlinear continuous and discrete models, formulated via random difference/differential/integral equations, random networks, etc., are powerful tools whose inputs (initial/boundary conditions, forcing terms, coefficients, adjacency matrix, etc.) require fixing initial probability distributions to computationally boot the model describing a particular complex system under analysis. This key task can be rigorously performed by applying inverse techniques and this point is particularly difficult in the context of models describing real complex systems. Furthermore, complexity may require using special operators (delay, fractional, etc.) able to capture memory or aftereffects in the context of random fluctuations. The outputs of such stochastic complex systems are usually described via some relevant statistics, such as the mean and the variance, addressed to describe the average behavior of the system as well as its variability. A more ambitious goal is to obtain the probability density function of outputs. In such a case, one can have a fuller probabilistic description of the complex system via higher statistical moments and one can calculate the probability that the output lies within an interval of interest. In this way, complex systems are better described, and hopefully characterized, as happens with Gaussian patterns via the computation of the mean and variance-covariance matrix. Apart from these issues, the analysis of complex systems with uncertainties lead to natural extensions of important concepts already studied in its deterministic counterpart like stochastic solitons, stochastic fractals, stochastic controllability, etc., whose complete understanding and methods are currently under intense investigation.

This special issue is devoted to consider substantially extended versions of papers presented at the conferenceICMMAS’19as well as external submissions, we require to gather relevant contributions addressed to introduce new techniques for study complex systems driven by random fluctuations. Contributions are expected to provide new insights by combining discrete/continuous models with uncertainty and computational techniques. Interdisciplinary applications are particularly welcome. More precisely, we will select the best contributions, after rigorous double-blind review, of papers dealing with important cut-edge advances in the realm of Complex Systems with Uncertainty and their Applications. We will put special emphasis on Nonlinear Science problems having physical insights and considering in their treatment stochastic approaches.

It is very important that the papers should have a highly level mathematical ground and satisfy CSF Aims and Scopes.

Potential topics include, but are not limited to:

Multiscale complex systems with uncertainties in computational Biology,

Nonlinear random games and networks with applications to model complex systems,

Discrete complex models driven by randomness,

Continuous complex models with randomness,

Random fractional differential equations and complex systems,

Fractional inverse problems and complex systems: Modeling and simulations,

Random solitons,

Stochastic fractal search,

Entropy and random behavior in nonlinear science,

Random nonlinear integrable systems in complex natural phenomena.

Qualitative properties of complex systems driven by uncertainty.

Modelling the dynamics of social phenomena via random nonlinear models.