We consider the problem of generating a matrix transfer function with prescribed strict bistability, biproperness, and positivity properties from a sequence of positive definite sample values at points on the frequency axis. We show how this arises in problems from multi-input/multioutput control analysis and design. This is a matrix interpolation problem with additional conditions, both on the...

Advances in molecular biology and the reduced costs in genetic modifications promoted the emergence of systems and synthetic biology over the last decade. In principle, these approaches can be applied on system level design for specific biological behavior through rewiring natural connectivity in the regulatory network. However, reality suggests otherwise: even for simple gene circuits, design ...

We use a biophysical model of a local neuronal circuit to study the implications of synaptic plasticity for the detection of weak sensory stimuli. Networks with fast plastic coupling show behavior consistent with stochastic resonance. The addition of an additional slow coupling that accounts for the asynchronous release of neurotransmitter results in qualitatively different properties of signal...

In addition to the well-known Rössler funnel that consists in near-homoclinic orbits, perfect homoclinic orbits have been found numerically and experimentally in a simplest piecewise linear Rössler-like electronic circuit. The evolution of the system in the homoclinic range exhibits period-bubbling and period-adding cascades when a control parameter is changed. A scaling law in the period-addin...

Optoelectronic hybrid bistability and multistability in an active interferometer using a laser diode are demonstrated experimentally. The active laser-diode interferometer is composed of a Twyman-Green interferometer with an electronic feedback circuit. By feeding back the interferometer output together with an external light input through a detector to control thelaser-diode injection current,...

A nonlinear electrical circuit is proposed as a basic cell for modeling FitzHugh-Nagumo neurons with a modified excitability. Depending on initial conditions and parameters experiments show various dynamics including stability with excitation, bistability and oscillations. Moreover, we present an electrical circuit which will be used to realize a unidirectional coupling between two cells, mimic...

Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining w...

Bistability in the lac operon of Escherichia coli has been widely studied, both experimentally and theoretically. Experimentally, bistability has been observed when E. coli is induced by an artificial, nonmetabolizable, inducer. However, if the lac operon is induced with lactose, the natural inducer, bistability has not been demonstrated. We derive an analytical expression that can predict the ...

Dual phosphorylation of proteins is a principal component of intracellular signalling. Bistability is considered an important property of such systems and its origin is not yet completely understood. Theoretical studies have established parameter values for multistationarity and bistability for many types of proteins. However, up to now no formal criterion linking multistationarity and bistabil...