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- Churilov, Alexander, et al.
(author)
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Mathematical model of non-basal testosterone regulation in the male by pulse modulated feedback
- 2009
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 45:1, s. 78-85
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Journal article (peer-reviewed)abstract
- A parsimonious mathematical model of pulse modulated regulation of non-basal testosterone secretion in the male is developed. The model is of the third differential order, reflecting the three most significant hormones in the regulation loop, but is yet shown to be capable of sustaining periodic solutions with one or two pulses of gonadotropin-releasing hormone (GnRH) in each period. Lack of stable periodic solutions is otherwise a main shortcoming of existing low-order hormone regulation models. Existence and stability of periodic solutions are studied. The periodic mode with two GnRH pulses in the least period has not been described in medical literature, but is found to explain experimental data well.
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| 4. |
- Churilov, Alexander, et al.
(author)
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Mathematical Model of Non-Basal Testosterone Regulation in the Male by Pulse Modulated Feedback
- 2007
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Reports (other academic/artistic)abstract
- A parsimonious mathematical model of pulse modulated regulation of non-basal testosterone secretion in the male is developed. The model is of third differential order, reflecting the three most significant hormones in the regulation loop, but is yet shown to be capable of sustaining periodic solutions with one or two pulses of gonadotropin-releasing hormone (GnRH) on each period. Lack of stable periodic solutions is otherwise a main shortcoming of existing low-order hormone regulation models. Existence and stability of periodic solutions are studied. The periodic mode with two GnRH pulses on the least period has not been described in medical literature but is found to explain experimental data well.
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- Churilov, Alexander N., et al.
(author)
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An impulse-to-impulse discrete-time mapping for a time-delay impulsive system
- 2014
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 50:8, s. 2187-2190
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Journal article (peer-reviewed)abstract
- It is shown that an impulsive system with a time-delay in the continuous part can be equivalently represented by discrete dynamics under less restrictive conditions on the time-delay value than considered previously.
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- Churilov, Alexander N., et al.
(author)
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Delay-induced Dynamical Phenomena in Impulsive Goodwin's Oscillator : What We Know So Far
- 2015
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In: 2015 54Th Ieee Conference On Decision And Control (CDC). - 9781479978861 ; , s. 590-595
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Conference paper (peer-reviewed)abstract
- Impulsive Goodwin's oscillator model is introduced to capture the dynamics of sustained periodic processes in endocrine systems controlled by episodic pulses of hormones. The model is hybrid and comprises a continuous subsystem describing the hormone concentrations operating under a discrete pulse-modulated feedback implemented by firing neurons. Time delays appear in mathematical models of endocrine systems due to the significant transport phenomena but also because of the time necessary to produce releasable hormone quantities. From a biological point of view, the neural control should be robust against the time delay to ensure the loop functionality over a wide range of inter-individual variability. The paper provides an overview of the currently available results and contributes a generalization of a Poincare mapping approach to study complex dynamics of impulsive Goodwin oscillator. Both pointwise and distributed time delays are considered in a general framework based on the Poincare mapping. Bifurcation analysis is utilized to illustrate the analytical results.
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- Churilov, Alexander N., et al.
(author)
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Discrete-time mapping for an impulsive Goodwin oscillator with three delays
- 2017
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In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 27:12
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Journal article (peer-reviewed)abstract
- A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis.
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