Željko Čupić

The chaotic sequences in the Bray–Liebhafsky reaction in an open reactor

Attractor reconstruction is done from the time series obtained by experimental investigation and by deterministic and stochastic simulation of the Bray-Liebhafsky oscillatory reaction. The appearance of deterministic chaos is confirmed and proven by both simulation and experiment, determining Lyapunov exponents for the sequences of flow rate values, as the control parameter. Moreover, unusual chaotic series were additionally recorded in the experiments, which cannot be found in deterministic numerical simulations. Therefore, an explanation of the difference between the dynamic behavior in the experiment and the deterministic simulation was sought and stochastic simulations based on the same reaction model were particularly useful. The fine structure of the chaotic windows, derived from the analysis of deterministic simulations in the range of flow rate values, made the system highly susceptible to noise induced effects, in general.

Modelling cholesterol effects on the dynamics of the hypothalamic-pituitary-adrenal (HPA) axis.

A mathematical model of the hypothalamic-pituitary-adrenal (HPA) axis with cholesterol as a dynamical variable was derived to investigate the effects of cholesterol, the primary precursor of all steroid hormones, on the ultradian and circadian HPA axis activity. To develop the model, the parameter space was systematically examined by stoichiometric network analysis to identify conditions for ultradian oscillations, determine conditions under which dynamic transitions, i.e. bifurcations occur and identify bifurcation types. The bifurcations were further characterized using numerical simulations. Model predictions agree well with empirical findings reported in the literature, indicating that cholesterol levels may critically affect the global dynamics of the HPA axis. The proposed model provides a base for better understanding of experimental observations, it may be used as a tool for designing experiments and offers useful insights into the characteristics of basic dynamic regulatory mechanisms that, when impaired, may lead to the development of some modern-lifestyle-associated diseases.

The Influence of the Isomerization Reactions on the Soybean Oil Hydrogenation Process

Abstract Soybean oil has been partially hydrogenated in the presence of a synthesized nickel catalyst, in an industrial reactor, under the standard industrial working conditions. The GC measurements of fatty acids in the investigated oil and hydrogenated products have been performed. The total trans isomers content has been determined by the IR spectroscopy. The model is established, which could be useful for the characterization of hydrogenation and isomerization reactions of poly-unsaturated acids. Iteration procedure, incorporating numerical simulation in each step is used to calculate rate constants of the proposed model from the comparison of the experimental and calculated kinetic runs. By the simultaneous treatment of the kinetic runs for the fatty acids composition and trans -isomer content, the 12 rate constants of individual hydrogenation and isomerization reaction steps are obtained.

Examinations of Cross-Linked Polyvinylpyridine in Open Reactor

Macroporous cross-linked copolymer of 4-vinylpyridine and 25% (4:1) divinylbenzene is analyzed under open conditions, that is in a continuous well-stirred tank reactor (CSTR). With this aim the appropriate bifurcation diagram is found and the behavior of the system with and without polymer in the vicinity of the bifurcation point is used for the polymer examinations. Two different granulations of polymer are considered. Moreover, some physicochemical characteristics of the polymer, such as specific surface area, skeletal and particle density, are determined.

Predictive Modeling of the Hypothalamic-Pituitary-Adrenal (HPA) Function. Dynamic Systems Theory Approach by Stoichiometric Network Analysis and Quenching Small Amplitude Oscillations

Two methods for dynamic systems analysis, Stoichiometric Network Analysis (SNA) and Quenching of Small Amplitude Oscillations (QA), are used to study the behaviour of a vital biological system. Both methods use geometric approaches for the study of complex reaction systems. In SNA, methods based on convex polytopes geometry are applied for stability analysis and optimization of reaction networks. QA relies on a geometric representation of the concentration phase space, introduces the concept of manifolds and the singular perturbation theory to study the dynamics of complex processes. The analyzed system, the Hypothalamic-Pituitary-Adrenal (HPA) axis, as a major constituent of the neuroendocrine system has a critical role in integrating biological responses in basal conditions and during stress. Self-regulation in the HPA system was modeled through a positive and negative feedback effect of cortisol. A systematically reduced low-dimensional model of HPA activity in humans was fine-tuned by SNA, until quantitative agreement with experimental findings was achieved. By QA, we revealed an important dynamic regulatory mechanism that is a natural consequence of the intrinsic rhythmicity of the considered system.

The stability of the extended model of hypothalamic-pituitary-adrenal axis examined by stoichiometric network analysis

Stoichiometric network analysis (SNA) represents a powerful mathematical tool for stability analysis of complex stoichiometric networks. Recently, the important improvement of the method has been made, according to which instability relations can be entirely expressed via reaction rates, instead of thus far used, in general case undefined, current rates. Such an improved SNA methodology was applied to the determination of exact instability conditions of the extended model of the hypothalamic-pituitary-adrenal (HPA) axis, a neuroendocrinological system, whose hormone concentrations exert complex oscillatory evolution. For emergence of oscillations, the Hopf bifurcation condition was utilized. Instability relations predicted by SNA showed good correlation with numerical simulation data of the HPA axis model.

Toluene Degradation in Water Using AlFe-Pillared Clay Catalysts

Abstract The catalytic wet peroxide oxidation (CWPO) of toluene on two bentonite-based AlFe-pillared clays (PILCs) with different iron contents was investigated. The PILCs were obtained using bentonite clay from Bogovina, Serbia. The change in chemical and phase composition and textural properties of the starting clay and synthesized catalysts was monitored using X-ray diffraction, inductively coupled plasma optical emission spectrometry, UV-Vis diffuse reflectance spectrometry, and physisorption of nitrogen. The catalytic performance was examined using gas chromatography. The Na-exchange process lowered the (001) smectite basal plane spacing, but the clay retained its swelling properties, while the pillaring process increased it. The surface areas of both synthesized pillared clays increased to values although their Fecontent was different. At 37 °C, both catalysts show significant toluene degradation, with the one richer in Fe having higher efficiency. The leaching of the active cations during reaction was negligible, and the catalysts were stable. AlFe-pillared clay catalysts can be used in CWPO for the elimination of BTEX compounds from plant effluent streams.

Contraction of the model for the Bray–Liebhafsky oscillatory reaction by eliminating intermediate I2O

The existing model for the Bray–Liebhafsky reaction aimed at simulating the largest possible number of various self-organization phenomena observed experimentally, is reduced herewith with the purpose of removing the intermediate I2O preserving the main characteristics of the parent model. The stoichiometric network analysis is applied.

Dynamic transitions in a model of the hypothalamic-pituitary-adrenal axis

Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations.

Dynamic behavior of the bray-liebhafsky oscillatory reaction controlled by sulfuric acid and temperature

The non-periodic, periodic and chaotic regimes in the Bray-Liebhafsky (BL) oscillatory reaction observed in a continuously fed well stirred tank reactor (CSTR) under isothermal conditions at various inflow concentrations of the sulfuric acid were experimentally studied. In each series (at any fixed temperature), termination of oscillatory behavior via saddle loop infinite period bifurcation (SNIPER) as well as some kind of the Andronov-Hopf bifurcation is presented. In addition, it was found that an increase of temperature, in different series of experiments resulted in the shift of bifurcation point towards higher values of sulfuric acid concentration.