In this paper, a delayed predator–prey epidemiological system with disease spreading in predator ... more In this paper, a delayed predator–prey epidemiological system with disease spreading in predator population is considered. By regarding the delay as the bifurcation parameter and analyzing the characteristic equation of the linearized system of the original system at the positive equilibrium, the local asymptotic stability of the positive equilibrium and the existence of local Hopf bifurcation of periodic solutions are investigated. Moreover, we also study the direction of Hopf bifurcations and the stability of bifurcated periodic solutions, an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.
Resume— L’analyse de la synchronisation d’oscillations est souvent modelisee a l’aide d’equations... more Resume— L’analyse de la synchronisation d’oscillations est souvent modelisee a l’aide d’equations differentielle qui decrivent la structure du systeme. L’ensemble des contraintes qui gouvernent la solution est condense en un systeme d’equations, dont la resolution est souvent tres difficile. Nous presentons une approche alternative par separation des contraintes. Nous envisageons ici l’impact de la seule contrainte de la congruence des frequences. Elle induit des formes qui sont autant « d’attracteurs » pour les familles de solutions. Ces formes ce deploient dans un espace d’evolution, que nous definissons. Nous analysons des singularites de congruences d’ordre 1 et 2. Dans l’espace d’evolution, nous proposons un scenario pour des series de bifurcations. Cette proposition est reliee a un exemple experimental, base sur un oscillateur de Van Der Pol. Enfin, pour les singularites de congruence d’ordre superieur a 2, nous exhibons le phenomene d’aplatissement des derivees. Mots cles—Bifurcations, congruence, synchronisation, contrainte, Van Der Pol. I. INTRODUCTION La synchronisation d’oscillations est utilisee da
This work presents an improved four-levels hierarchical control strategy for flexible microgrid b... more This work presents an improved four-levels hierarchical control strategy for flexible microgrid based on three-phase voltage source inverters (VSIs) connected in parallel. In the proposed strategy, zero-level control is required to handle current and voltage control of VSIs. The primary-level that consists of a decentralized controller is based on a modified universal droop control by introducing a fractional-order derivative. It is used to enhance the power sharing quality during islanded mode and the desired power generation in grid-connected mode. In the secondary centralized control, the voltage and frequency deviations caused by the primary-control are restored. Also, this level includes the synchronization control loop that enables a seamless transition between both operation modes. In order to improve the flexibility of the microgrid, a sequential logic approach is proposed in the tertiary level. It is exploited to manage both the restoration and the synchronization loops at ...
In this paper, sliding mode observers are designed in order to estimate actuator and sensor fault... more In this paper, sliding mode observers are designed in order to estimate actuator and sensor faults for linear fractional-order systems. The system is represented by a commensurate fractional-order state space model, in the presence of unknown sensor and actuator faults. The convergence of the designed observers is established. A numerical example is given to illustrate the effectiveness of the proposed approach.
In this paper, a delayed predator–prey epidemiological system with disease spreading in predator ... more In this paper, a delayed predator–prey epidemiological system with disease spreading in predator population is considered. By regarding the delay as the bifurcation parameter and analyzing the characteristic equation of the linearized system of the original system at the positive equilibrium, the local asymptotic stability of the positive equilibrium and the existence of local Hopf bifurcation of periodic solutions are investigated. Moreover, we also study the direction of Hopf bifurcations and the stability of bifurcated periodic solutions, an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.
Resume— L’analyse de la synchronisation d’oscillations est souvent modelisee a l’aide d’equations... more Resume— L’analyse de la synchronisation d’oscillations est souvent modelisee a l’aide d’equations differentielle qui decrivent la structure du systeme. L’ensemble des contraintes qui gouvernent la solution est condense en un systeme d’equations, dont la resolution est souvent tres difficile. Nous presentons une approche alternative par separation des contraintes. Nous envisageons ici l’impact de la seule contrainte de la congruence des frequences. Elle induit des formes qui sont autant « d’attracteurs » pour les familles de solutions. Ces formes ce deploient dans un espace d’evolution, que nous definissons. Nous analysons des singularites de congruences d’ordre 1 et 2. Dans l’espace d’evolution, nous proposons un scenario pour des series de bifurcations. Cette proposition est reliee a un exemple experimental, base sur un oscillateur de Van Der Pol. Enfin, pour les singularites de congruence d’ordre superieur a 2, nous exhibons le phenomene d’aplatissement des derivees. Mots cles—Bifurcations, congruence, synchronisation, contrainte, Van Der Pol. I. INTRODUCTION La synchronisation d’oscillations est utilisee da
This work presents an improved four-levels hierarchical control strategy for flexible microgrid b... more This work presents an improved four-levels hierarchical control strategy for flexible microgrid based on three-phase voltage source inverters (VSIs) connected in parallel. In the proposed strategy, zero-level control is required to handle current and voltage control of VSIs. The primary-level that consists of a decentralized controller is based on a modified universal droop control by introducing a fractional-order derivative. It is used to enhance the power sharing quality during islanded mode and the desired power generation in grid-connected mode. In the secondary centralized control, the voltage and frequency deviations caused by the primary-control are restored. Also, this level includes the synchronization control loop that enables a seamless transition between both operation modes. In order to improve the flexibility of the microgrid, a sequential logic approach is proposed in the tertiary level. It is exploited to manage both the restoration and the synchronization loops at ...
In this paper, sliding mode observers are designed in order to estimate actuator and sensor fault... more In this paper, sliding mode observers are designed in order to estimate actuator and sensor faults for linear fractional-order systems. The system is represented by a commensurate fractional-order state space model, in the presence of unknown sensor and actuator faults. The convergence of the designed observers is established. A numerical example is given to illustrate the effectiveness of the proposed approach.
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Papers by Jean-Pierre Barbot