Synchronization is a widespread phenomenon in both synthetic and real-world networks.This collective behavior of simple and complex systems has been attracting much research during the last decades.Two different route...Synchronization is a widespread phenomenon in both synthetic and real-world networks.This collective behavior of simple and complex systems has been attracting much research during the last decades.Two different routes to synchrony are defined in networks;first-order,characterized as explosive,and second-order,characterized as continuous transition.Although pioneer researches explained that the transition type is a generic feature in the networks,recent studies proposed some frameworks in which different phase and even chaotic oscillators exhibit explosive synchronization.The relationship between the structural properties of the network and the dynamical features of the oscillators is mainly proclaimed because some of these frameworks show abrupt transitions.Despite different theoretical analyses about the appearance of the firstorder transition,studies are limited to the mean-field theory,which cannot be generalized to all networks.There are different real-world and man-made networks whose properties can be characterized in terms of explosive synchronization,e.g.,the transition from unconsciousness to wakefulness in the brain and spontaneous synchronization of power-grid networks.In this review article,explosive synchronization is discussed from two main aspects.First,pioneer articles are categorized from the dynamical-structural framework point of view.Then,articles that considered different oscillators in the explosive synchronization frameworks are studied.In this article,the main focus is on the explosive synchronization in networks with chaotic and neuronal oscillators.Also,efforts have been made to consider the recent articles which proposed new frameworks of explosive synchronization.展开更多
The fractional order model of a glucose-insulin regulatory system is derived and presented. It has been extensively proved in the literature that fractional order analysis of complex systems can reveal interesting and...The fractional order model of a glucose-insulin regulatory system is derived and presented. It has been extensively proved in the literature that fractional order analysis of complex systems can reveal interesting and unexplored features of the system. In our investigations we have revealed that the glucose-insulin regulatory system shows multistability and antimonotonicity in its fractional order form. To show the effectiveness of fractional order analysis, all numerical investigations like stability of the equilibrium points, Lyapunov exponents, and bifurcation plots are derived. Various biological disorders caused by an unregulated glucose-insulin system are studied in detail. This may help better understand the regulatory system.展开更多
文摘Synchronization is a widespread phenomenon in both synthetic and real-world networks.This collective behavior of simple and complex systems has been attracting much research during the last decades.Two different routes to synchrony are defined in networks;first-order,characterized as explosive,and second-order,characterized as continuous transition.Although pioneer researches explained that the transition type is a generic feature in the networks,recent studies proposed some frameworks in which different phase and even chaotic oscillators exhibit explosive synchronization.The relationship between the structural properties of the network and the dynamical features of the oscillators is mainly proclaimed because some of these frameworks show abrupt transitions.Despite different theoretical analyses about the appearance of the firstorder transition,studies are limited to the mean-field theory,which cannot be generalized to all networks.There are different real-world and man-made networks whose properties can be characterized in terms of explosive synchronization,e.g.,the transition from unconsciousness to wakefulness in the brain and spontaneous synchronization of power-grid networks.In this review article,explosive synchronization is discussed from two main aspects.First,pioneer articles are categorized from the dynamical-structural framework point of view.Then,articles that considered different oscillators in the explosive synchronization frameworks are studied.In this article,the main focus is on the explosive synchronization in networks with chaotic and neuronal oscillators.Also,efforts have been made to consider the recent articles which proposed new frameworks of explosive synchronization.
基金Project supported by the Institute of Research and Development,Defence University,Ethiopia(No.DU/IRD/002)。
文摘The fractional order model of a glucose-insulin regulatory system is derived and presented. It has been extensively proved in the literature that fractional order analysis of complex systems can reveal interesting and unexplored features of the system. In our investigations we have revealed that the glucose-insulin regulatory system shows multistability and antimonotonicity in its fractional order form. To show the effectiveness of fractional order analysis, all numerical investigations like stability of the equilibrium points, Lyapunov exponents, and bifurcation plots are derived. Various biological disorders caused by an unregulated glucose-insulin system are studied in detail. This may help better understand the regulatory system.
