• Advances in nano research
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• 제10권4호
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• pp.359-371
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• 2021

A tumor immune interaction is a main topic of interest in the last couple of decades because majority of human population suffered by tumor, formed by the abnormal growth of cells and is continuously interacted with the immune system. Because of its wide range of applications, many researchers have modeled this tumor immune interaction in the form of ordinary, delay and fractional order differential equations as the majority of biological models have a long range temporal memory. So in the present work, tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and interleukin-2 (IL-2) are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Furthermore, existence and local stability of fixed points are investigated for discrete model. Moreover, it is proved that two types of bifurcations such as Neimark-Sacker and flip bifurcations are studied. Finally, numerical examples are presented to support our analytical results.

• Journal of Power Electronics
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• 제19권5호
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• pp.1108-1121
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• 2019

The non-inverting buck-boost converter (NIBB) is a step-up and step-down DC-DC converter suitable for wide-input-voltage-range applications. However, when the input voltage is close to the output voltage, the NIBB needs to operate in the buck-boost mode, causing a significant efficiency reduction since all four switches operates in the PWM mode. Considering both the current stress limitation and the efficiency optimization, a novel design methodology for the optimal phase-shift modulation of a NIBB in the buck-boost mode is proposed in this paper. Since the four switches in the NIBB form two bridges, the shifted phase between the two bridges can serve as an extra degree of freedom for performance optimization. With general phase-shift modulation, the analytic current expressions for every duty ratio, shifted phase and input voltage are derived. Then with the two key factors in the NIBB, the converter efficiency and the switch current stress, taken into account, an objective function with constraints is derived. By optimizing the derived objective function over the full input voltage range, an offline design methodology for the optimal modulation scheme is proposed for efficiency optimization on the premise of current stress limitation. Finally, the designed optimal modulation scheme is implemented on a DSPs and the design methodology is verified with experimental results on a 300V-1.5kW NIBB prototype.