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The common goal of systems pharmacology, i.e. systems biology applied to the field of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens . (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system...
In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented...
The paper presents an algorithm for the solution of the consensus problem of a linear multi-agent system composed of identical agents. The control of the agents is delayed, however, these delays are, in general, not equal in all agents. The control algorithm design is based on the -control, the results are formulated by means of linear matrix inequalities. The dimension of the resulting convex optimization problem is proportional to the dimension of one agent only but does not depend on the number...
The problem of stabilization of large-scale systems and the consensus problem of multi-agent systems are related, similar tools for their solution are used. Therefore, they are occasionally confused. Although both problems show similar features, one can also observe important differences. A comparison of both problems is presented in this paper. In both cases, attention is paid to the explanation of the effects of the time delays. The most important fact is that, if the time delays are heterogeneous,...
We develop and test a relatively simple enhancement of the classical model reduction method applied to a class of chemical networks with mass conservation properties. Both the methods, being (i) the standard quasi-steady-state approximation method, and (ii) the novel so-called delayed quasi-steady-state approximation method, firstly proposed by Vejchodský (2014), are extensively presented. Both theoretical and numerical issues related to the setting of delays are discussed. Namely, for one slightly...
The well-known bottleneck of systems pharmacology, i. e., systems biology applied to pharmacology, refers to the model parameters determination from experimentally measured datasets. This paper represents the development of our earlier studies devoted to inverse (ill-posed) problems of model parameters identification. The key feature of this research is the introduction of control (or periodic forcing by an input signal being a drug intake) of the nonlinear model of drug-induced enzyme production...
Generalized synchronization in the direct acyclic networks, i.e. the networks represented by the directed tree, is presented here. Network nodes consist of copies of the so-called generalized Lorenz system with possibly different parameters yet mutually structurally equivalent. The difference in parameters actually requires the generalized synchronization rather than the identical one. As the class of generalized Lorenz systems includes the well-known particular classes such as (classical) Lorenz...
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