Mathematical modeling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations (QSSA). A QSSA theorem is applied to a modified mathematical model of the microRNA-mediated protein translation process. By an appropriate normalized procedure the system of seven nonlinear ordinary differential equations is rewritten in a f...

We describe a new probabilistic model for learning of coupled dynamical systems in latent state spaces. The coupling is achieved by combining predictions from several Gaussian process dynamical models in a product-of-experts fashion. Our approach facilitates modulation of coupling strengths without the need for computationally expensive re-learning of the dynamical models. We demonstrate the ef...

A quite general interaction process within a multi-component system is analysed by the extended effective potential method liberated from usual limitations of perturbation theory or integrable model. The obtained causally complete solution of the many-body problem reveals the phenomenon of dynamic multivaluedness, or redundance, of emerging, incompatible system realisations and dynamic entangle...

In this paper, the modeling of a dynamic chemical engineering process is presented in a highly understandable way using a unique combination of the simplified fundamental theory and direct hands-on computer simulation. The main aim is to use them for analysis, optimise and adaptive control of behavior of dynamical system, especially of a given chemical reactor. A non-linear mathematical model i...

A new Chemo Dynamical Smoothed Particle Hydrodynamic (CD SPH) code is presented. The disk galaxy is described as a multi fragmented gas and star system, embedded in a cold dark matter halo. The star formation (SF) process, SNII, SNIa and PN events as well as chemical enrichment of gas have been considered within the framework of the standard SPH model. Using this model we describe the dynamical...

Liu process is an uncertain process with stationary and independent increments. Multi-dimensional uncertain differential equation is a type of differential equation driven by multi-dimensional Liu process to model a multidimensional dynamic system. This paper aims at proposing a definition of stability in mean for multi-dimensional uncertain differential equations. Then a stability theorem for ...

 In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...

We study the interplay between a dynamical process and the structure of the network on which it unfolds using the parameterized Laplacian framework. This framework allows for defining and characterizing an ensemble of dynamical processes on a network beyond what the traditional Laplacian is capable of modeling. This, in turn, allows for studying the impact of the interaction between dynamics an...

In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied.  The invariance of the {it logic entropy} of a system  under isomorphism is proved. At the end,  the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...

Most mathematical models used to understand the dynamical patterns seen in the incidence of childhood viral diseases, such as measles, employ a simple, but epidemiologically unrealistic, description of the infection and recovery process. The inclusion of more realistic descriptions of the recovery process is shown to cause a significant destabilization of the model. When there is seasonal varia...