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The name field is required. Please enter your name. The E-mail message field is required. Please enter the message. In this case, the metabolic system shifts condition from absorptive to postabsorptive [ 11 , 12 ]. As delineated in the preceding paragraph, various mathematical models have been proposed in attempts to simulate the relation between plasma glucose concentration and plasma insulin concentration more accurately, so that scientists will be able to have an elaborate perspective of this metabolic interaction [ 13 — 17 ].
It is wondering that the recently submitted models show some kind of chaotic behavior in the mechanism of malfunctioning metabolic system which is revealed in the current study. The investigation of chaotic dynamics has attracted the foci of many scientists, and a great deal of effort is put in this field as it has provided a successful method for studying biological systems [ 18 — 23 ].
Moreover, this novel vantage point of studying biological phenomena has made revolutionary effects on developing biological system models [ 24 — 27 ]. Because of the complexity of the system, the model that has been studied in this paper is a nonlinear model. The nonlinear model that we study reflects the relationship between injected insulin and blood glucose response. The studies about variation in the blood glucose indicate a chaotic component. In the second section, the dynamical properties of the last presented model for glucose and insulin concentration are investigated.
Eventually, conclusion remarks are given in Section 4. In , Ackerman et al. In , Bajaj et al. Recent studies indicate two delays in glucose-insulin feedback control system [ 28 — 32 ]. Two important time lags can be noticed in the system, the lag in insulin secretion in response to an increase in blood glucose concentration, , and hepatic glucose response lag,. The modified model is the compound of the model proposed by Bajaj et al. The resulted model is the one presented by Chuedoung et al. System 3 considers two time lags in insulin-glucose regulatory system; therefore, it is more realistic and is capable of showing the behavior of insulin-glucose regulatory system in different time delays.
Previous models cannot display the behavior of aforementioned biological system with respect to time delays. According to the model presented by Molnar et al.
The term represents the increase in due to interaction between dividing and nondividing -cells, and the term represents the reduction in due to its current level. Based on the study by Chuedoung et al. The proposed model comprises a number of parameters that their values are essential in changing the behavior of the system.
Chaos, complexity and leadership 2012
In current research, the new capability of the mentioned model is revealed. By increasing the insulin secretion delay by -cells , the system behaves in a chaotic way Figure 2. Figure 2 is the bifurcation diagram of the system for the different values of. Figure 2 shows that if there is more delay on insulin secretion, insulin cannot track glucose and the concentration of blood glucose rises which results in diabetes disorder.
Technically speaking, the time lag of insulin response in glucose-insulin negative feedback controlling mechanism is shown to be the main reason for this disease. Computer simulation of Figure 2 is done by the following parameters , , , , , , , , , , , , and. The values of the parameters are the same as the values presented by Chuedoung et al. With the increase in glucose response time caused by insulin secretion , the system behaves chaotically Figure 3.
Figure 3 is the bifurcation diagram of the system for different values of. It shows that if there is more delay on response of glucose to insulin secretion, the system behaves in a chaotic manner. Note that the goal of this study is not to investigate the parameters quantitatively, but rather to show that a minute change in the quantities of parameters of the model can bring about changes in the behavior of the system. Computer simulation of Figure 3 is done by the following parameters , , , , , , , , , , , , and. The system is stable for small delays, and when the delays increase, the system exhibits chaotic behavior.
And, based on a report by Forrest et al. The response time was about 1 minute for them; whereas, this delay ranged from 5 to 10 minutes for the other children. Hence, these observations support our claim about the range of and. A new sliding mode control scheme for a class of uncertain time-delay chaotic systems is proposed in [ 37 ].
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It is shown that a linear time-invariant system with the desired system dynamics is used as a reference model for the output of a time-delay chaotic system to track. Chaos control for scalar-delayed chaotic systems using sliding mode control strategy is achieved in [ 38 ]. Sliding surface design is based on delayed feedback controller, and it is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point UPF or unstable periodic orbit UPO with an arbitrary period.
In this section, we design the adaptive sliding mode controllers to suppress the chaotic oscillations in the model presented in 3. For the uncertainties, we assume that the parameters and are unknown. The entire control algorithm is designed with the delay elements as described in 3 , and hence the sliding surface initialization is accounted with the respective time delays.
Let us redefine the model in 3 with the controllers , where as given in. Contents of the book are composed from broad range of chaos, complexity and their applications in multi disciplines. Articles reflect different perspectives in the field of applied nonlinear methods, modeling of data and simulations as well as theoretical achievements of chaos and complex systems.
Chaos, Complexity and Leadership 2012
In addition to this, readers are going to find new applications in leadership and management of chaos and complexity theory such as in fields from education to politics. It is completely new and fresh piece of mind for readers who are interested in chaos, complexity and especially leadership.
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