Paul Woafo

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A linear chain of cells is considered in which calcium (Ca2+) fluctuations within a cell are described by a simple minimal model. Cells are coupled together by bidirectional paracrine signaling via calcium oscillations. Two typical zones of propagation are observed: a transition zone and a regular zone. The transition zone exhibits the same phenomena that(More)
We study the spatiotemporal dynamics of a ring of diffusely coupled single-well Duffing oscillators. The transitions from spatiotemporal chaos to cluster and complete synchronization states are particularly investigated, as well as the Hopf bifurcations to instability. It is found that the underlying mechanism of these transitions relies on the motion of(More)
This paper considers the synchronization dynamics in a ring of four mutually coupled biological systems described by coupled Van der Pol oscillators. The coupling parameter are non-identical between oscillators. The stability boundaries of the process are first evaluated without the influence of the local injection using the eigenvalues properties and the(More)
We consider the problem of stability and duration of the synchronization process between self-excited oscillators, both in their regular and chaotic states. Making use of the properties of Hill equation describing the deviation between the slave and the master, we derive the stability conditions and expressions of the synchronization time. A fairly good(More)
We investigate in this paper different states of synchronization in a ring of mutually coupled self-sustained electrical oscillators. The good coupling parameters leading to complete and partial synchronization or disordered states are calculated using the properties of the variational equations of stability. A stability map showing domains of(More)
In this paper, we study the spatiotemporal dynamics of a ring of diffusely coupled nonlinear oscillators. Floquet theory is used to investigate the various dynamical states of the ring, as well as the Hopf bifurcations between them. A local injection scheme is applied to synchronize the ring with an external master oscillator. The shift-invariance symmetry(More)
We investigate the conditions under which an optimal continuous feedback control can be achieved. Chaotic oscillations in the single-well Duffing model, with either a positive or a negative nonlinear stiffness term, are tuned to their related Ritz approximation. The Floquet theory enables the stability analysis of the control. Critical values of the(More)
We perform a stability and optimization analysis for the synchronization of unidirectionally coupled external-cavity semiconductor lasers. Using rigorous stability criteria, we qualitatively derive the boundaries of the high-quality synchronization basin. The underlying influence of Hopf bifurcations on the stability of the synchronization manifold is also(More)