Bounded Noises in Physics, Biology, and Engineering

Since the parameters in dynamical systems of biological interest are inherently positive and bounded, bounded noises are a natural way to model the realistic stochastic fluctuations of a biological system that are caused by its interaction with the external world. Bounded Noises in Physics, Biology, and Engineering is the first contributed volume devoted to the modeling of bounded noises in theoretical and applied statistical mechanics, quantitative biology, and mathematical physics. It gives an overview of the current state-of-the-art and is intended to stimulate further research.

The volume is organized in four parts. The first part presents the main kinds of bounded noises and their applications in theoretical physics. The theory of bounded stochastic processes is intimately linked to its applications to mathematical and statistical physics, and it would be difficult and unnatural to separate the theory from its physical applications. The second is devoted to framing bounded noises in the theory of random dynamical systems and random bifurcations, while the third is devoted to applications of bounded stochastic processes in biology, one of the major areas of potential applications of this subject. The final part concerns the application of bounded stochastic processes in mechanical and structural engineering, the area where the renewed interest for non-Gaussian bounded noises started. Pure mathematicians working on stochastic calculus will find here a rich source of problems that are challenging from the point of view of contemporary nonlinear analysis.

Bounded Noises in Physics, Biology, and Engineering is intended for scientists working on stochasticprocesses with an interest in both fundamental issues and applications. It will appeal to a broad range of applied mathematicians, mathematical biologists, physicists, engineers, and researchers in other fields interested in complexity theory. It is accessible to anyone with a working knowledge of stochastic modeling, from advanced undergraduates to senior researchers.

Introduction.- Part I : Modeling of Bounded Noises and Their Applications in Physics.- On Bounded Stochastic Processes.- Dynamics of Systems With Randomly Disordered Periodic Excitations.- Noise-Induced Phenomena: Effects of Noises Based on Tsallis Statistics.- Dynamical Systems Driven by Dichotomous Noise.- Stochastic Oscillator : Brownian Motion With Adhesion.- Numerical Study of Energetic Stability For Harmonic Oscillator With Fluctuating Damping Parameter.- A Moment-Based Approach to Bounded Non-Gaussian Colored Noise.- Spatiotemporal Bounded Noises, and Their Application to the Ginzburg-Landau Equation.- Part II: Bounded Noises in the Framework of Discrete and Continuous Random Dynamical Systems.- Bifurcations of Random Differential Equations With Bounded Noise.- Effects of Bounded Random Perturbations on Discrete Dynamical Systems.- Part III: Bounded Stochastic Fluctuations in Biology.- Bounded Stochastic Perturbations May Induce Non-Genetic Resistance to Anti-Tumor Chemotherapy.- Interplay Between Cross Correlation and Delays in the Sine-Wienernoise-Induced Transitions.- Bounded Extrinsic Noises Affecting Biochemical Networks With Low Molecule Numbers.- Part IV: Bounded Noises: Applications in Engineering.- Almost Sure Stability of Fractional Viscoelastic Systems Driven By Bounded Noises.- Model Selection for Random Functions With Bounded Range. Applications in Science and Engineering.- From Model-Based to Data-Driven Filter Design.