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Models for the transmission of the chikungunya virus to human population are discussed. The chikungunya virus is an alpha arbovirus, first identified in 1953. It is transmitted by Aedes mosquitoes and is responsible for a little documented uncommon acute tropical disease. Models describing the mosquito population dynamics and the virus transmission to the(More)
we present a two-dimensional continuous time dynamical system modeling a predator-prey food chain, and based on's modified version of the Leslie-Gower scheme and on the Holling-type II scheme. The main result i$ given in terms of boundedness of solutions, existence of an attracting set and global stability of the coexisting interior equilibrium.
We consider a FitzHugh-Nagumo Reaction-Diffusion type system (FHN). The dynamics of the reaction part induces a unique repulsive stationnary point (0, 0) and a unique attractive limit cycle. After a description of the asymptotic behaviour of the FHN system, we deal with the synchronization and control analysis of N coupled FHN systems.
Synovial hemangioma of the knee joint was diagnosed in a young woman 15 years after the first signs. The principal clinical manifestation involved repeated episodes of hemorrhagic joint effusion. MRI is the exploration of choice for this vascular tumor of the synovial membrane, although a pathology study is needed to confirm the diagnosis. Cure is achieved(More)
The differential transform method (DTM) is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form. In this paper, we propose a reliable new algorithm of DTM, namely multi-step DTM, which will increase the interval of convergence for the series solution. The multi-step DTM is(More)
The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear(More)
A fairly realistic three-species food-chain model based on Lotka±Volterra and Leslie±Gower schemes is investigated assuming that just a single scalar time series is available. The paper uses tools borrowed from the theory of nonlinear dynamical systems. The quality of the di€erent phase portraits reconstructed is tested. Such a situation would arise in(More)
Since the 1980s, there has been a worldwide re-emergence of vector-borne diseases including Malaria, Dengue, Yellow fever or, more recently, chikungunya. These viruses are arthropod-borne viruses (arboviruses) transmitted by arthropods like mosquitoes of Aedes genus. The nature of these arboviruses is complex since it conjugates human, environmental,(More)
We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It(More)
The aim of this paper is to contribute to the modeling and analysis of complex systems, taking into account the nature of complexity at different stages of the system life-cycle: from its genesis to its evolution. Therefore, some structural aspects of the complexity dynamics are highlighted, leading (i) to implement the morphogenesis of emergent complex(More)