Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …

We present a mathematical analysis of a networks with Integrate-and-Fire neurons with
conductance based synapses. Taking into account the realistic fact that the spike time is only …

Complex networks of dynamically connected saddle states persistently emerge in a broad
range of high-dimensional systems and may reliably encode inputs as specific switching …

On the robustness of chaos in dynamical systems:Theories and applications Page 1 On the
robustness of chaos in dynamical systems:Theories and applications Zeraoulia Elhadj1, JC …

Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in
the form of attracting yet unstable saddle periodic orbits where units are synchronized into …

Heteroclinic computing offers a novel paradigm for universal computation by collective
system dynamics. In such a paradigm, input signals are encoded as complex periodic orbits …

The phenomenon of resonance will be dealt with from the viewpoint of dynamical systems
depending on parameters and their bifurcations. Resonance phenomena are associated to …

Symmetric networks of coupled dynamical units exhibit invariant subspaces with two or more
units synchronized. In time-continuously coupled systems, these invariant sets constitute …

We consider networks of pulse coupled linear oscillators with non-zero delay where the
coupling between the oscillators is given by the Mirollo–Strogatz function. We prove the …

We show that unstable attractors do not exist for smooth invertible dynamics. In systems
lacking these properties, we draw simple conclusions about their stability indices and look at …