This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system wi...This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium.Through phase portrait,bifurcation diagrams,and largest Lyapunov exponents,it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors.Also,different tests are used to confirm the existence of chaos,such as 0-1 test and C0 complexity.In addition,the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique.Furthermore,based on the fractional linearization method,a one-dimensional controller to stabilize the new system is proposed.Numerical results are presented to validate the findings of the paper.展开更多
The economic and financial systems consist of many nonlinear factors that make them behave as the complex systems.Recently many chaotic finance systems have been proposed to study the complex dynamics of finance as a ...The economic and financial systems consist of many nonlinear factors that make them behave as the complex systems.Recently many chaotic finance systems have been proposed to study the complex dynamics of finance as a noticeable problem in economics.In fact,the intricate structure between financial institutions can be obtained by using a network of financial systems.Therefore,in this paper,we consider a ring network of coupled symmetric chaotic finance systems,and investigate its behavior by varying the coupling parameters.The results show that the coupling strength and range have significant effects on the behavior of the coupled systems,and various patterns such as the chimera and multi-chimera states are observed.Furthermore,changing the parameters'values,remarkably influences on the oscillators attractors.When several synchronous clusters are formed,the attractors of the synchronized oscillators are symmetric,but different from the single oscillator attractor.展开更多
Parkinson’s and Huntington’s diseases are two of the most common neurodegenerative disorders. Tremor,muscle stiffness, and slowness of movement are symptoms of Parkinson’s disease. The symptoms of Huntington’s dis...Parkinson’s and Huntington’s diseases are two of the most common neurodegenerative disorders. Tremor,muscle stiffness, and slowness of movement are symptoms of Parkinson’s disease. The symptoms of Huntington’s disease are severe reduction in muscle control, emotional disturbance, and pathological disorders in brain cells. These diseases are caused by destruction of the cells that secrete a substance called dopamine. In this paper, a new discrete chaotic system is introduced, which can mimic the brain’s behavior for neurodegenerative diseases such as Parkinson, Huntington, and Hypokinesia. This system is described based on the similarity between the brain’s behavior in normal and abnormal conditions and the chaotic systems. Bifurcation analysis is carried out with respect to different parameters, providing full spectrum of the behavior for different parameter values. Our results can be used to mathematically study the mechanisms behind these diseases.展开更多
Chimera state is a peculiar spatiotemporal pattern,wherein the coherence and incoherence coexist in the network of coupled identical oscillators.In this paper,we study the chimera states in a network of impact oscilla...Chimera state is a peculiar spatiotemporal pattern,wherein the coherence and incoherence coexist in the network of coupled identical oscillators.In this paper,we study the chimera states in a network of impact oscillators with nonlocal coupling.We investigate the effects of the coupling strength and the coupling range on the network behavior.The results reveal the emergence of the chimera state for significantly small values of coupling strength,and higher coupling strength values lead to unbounded motions in the oscillators.We also study the network in the case of excitation failure.We observe that the coupling helps in the maintenance of an oscillatory motion with a lower amplitude in the failed oscillator.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
基金The author Adel Ouannas was supported by the Directorate General for Scientific Research and Technological Development of Algeria.The author Shaher Momani was supported by Ajman University in UAE.
文摘This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium.Through phase portrait,bifurcation diagrams,and largest Lyapunov exponents,it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors.Also,different tests are used to confirm the existence of chaos,such as 0-1 test and C0 complexity.In addition,the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique.Furthermore,based on the fractional linearization method,a one-dimensional controller to stabilize the new system is proposed.Numerical results are presented to validate the findings of the paper.
文摘The economic and financial systems consist of many nonlinear factors that make them behave as the complex systems.Recently many chaotic finance systems have been proposed to study the complex dynamics of finance as a noticeable problem in economics.In fact,the intricate structure between financial institutions can be obtained by using a network of financial systems.Therefore,in this paper,we consider a ring network of coupled symmetric chaotic finance systems,and investigate its behavior by varying the coupling parameters.The results show that the coupling strength and range have significant effects on the behavior of the coupled systems,and various patterns such as the chimera and multi-chimera states are observed.Furthermore,changing the parameters'values,remarkably influences on the oscillators attractors.When several synchronous clusters are formed,the attractors of the synchronized oscillators are symmetric,but different from the single oscillator attractor.
文摘Parkinson’s and Huntington’s diseases are two of the most common neurodegenerative disorders. Tremor,muscle stiffness, and slowness of movement are symptoms of Parkinson’s disease. The symptoms of Huntington’s disease are severe reduction in muscle control, emotional disturbance, and pathological disorders in brain cells. These diseases are caused by destruction of the cells that secrete a substance called dopamine. In this paper, a new discrete chaotic system is introduced, which can mimic the brain’s behavior for neurodegenerative diseases such as Parkinson, Huntington, and Hypokinesia. This system is described based on the similarity between the brain’s behavior in normal and abnormal conditions and the chaotic systems. Bifurcation analysis is carried out with respect to different parameters, providing full spectrum of the behavior for different parameter values. Our results can be used to mathematically study the mechanisms behind these diseases.
基金Project supported by the Polish National Science Centre,MAESTRO Programme(No.2013/08/A/ST8/00780)the OPUS Programme(No.2018/29/B/ST8/00457)。
文摘Chimera state is a peculiar spatiotemporal pattern,wherein the coherence and incoherence coexist in the network of coupled identical oscillators.In this paper,we study the chimera states in a network of impact oscillators with nonlocal coupling.We investigate the effects of the coupling strength and the coupling range on the network behavior.The results reveal the emergence of the chimera state for significantly small values of coupling strength,and higher coupling strength values lead to unbounded motions in the oscillators.We also study the network in the case of excitation failure.We observe that the coupling helps in the maintenance of an oscillatory motion with a lower amplitude in the failed oscillator.
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.
