In the present work, we combine concepts and tools from Irreversible Thermodynamics and Control Theory in a contribution to unravel the origin of complex nonlinear behaviour in biochemical networks. Regarding cells as thermodynamic systems, we can consider dynamic evolution of intracellular processes in terms of the combined action of an endogenous entropy production and the entropy flux associ...

The potential flow equations which govern the free–surface motion of an ideal fluid (the water wave problem) are notoriously difficult to solve for a number of reasons. First, they are a classical free– boundary problem where the domain shape is one of the unknowns to be found. Additionally, they are strongly nonlinear (with derivatives appearing in the nonlinearity) without a natural dissipati...

This paper presents two nonlinear model-based control designs for a hydraulic system that consists of two mechanically coupled hydraulic cylinders actuated each by a separate servo-valve. Based on a physically-oriented nonlinear mathematical model of the test rig, a further model simplification results in a completely controllable MIMO system. Two different control structures are discussed and ...

We consider the problem of decoding block coded data, using a physical dynamical system. We sketch out a decompression algorithm for fractal block codes and then show how to implement a recurrent neural network using physically simple but highly-nonlinear, analog circuit models of neurons and synapses. The nonlinear system has many fixed points, but we have at our disposal a procedure to choose...

We focus on the morphochemical reaction-diffusion model introduced in [13] and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns close to the marginal stability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis for both the 1D and 2D spatial case, deriving the equations for the amplitu...

To understand the solution of a linear, time-invariant differential-algebraic equation (DAE), one must analyze a matrix pencil (A,E) with singular E. Even when this pencil is stable (all its finite eigenvalues fall in the left half-plane), the solution can exhibit transient growth before its inevitable decay. When the equation results from the linearization of a nonlinear system, this transient...

The nonlinear Schrödinger equation i (partial differential)(z)A(z,x,t)+(inverted Delta)(2)(x,t)A+[1+m(kappax)]|A|2A=0 models the propagation of ultrashort laser pulses in a planar waveguide for which the Kerr nonlinearity varies along the transverse coordinate x, and also the evolution of 2D Bose-Einstein condensates in which the scattering length varies in one dimension. Stability of bound sta...

Three studies were conducted to evaluate a prototype nonlinear digital beamforming hearing aid. The experiments all used contextually rich speech materials and subjective analysis methods and, on that basis, are grouped together in this report. In experiment 1, the beamforming was done off line and subjects wore their own hearing aids in an attempt to determine whether the processing reduced th...

The long wave–short wave resonance model arises physically when the phase velocity of a long wave matches the group velocity of a short wave. It is a system of nonlinear evolution equations solvable by the Hirota bilinear method and also possesses a Lax pair formulation. ‘‘Rogue wave’’ modes, algebraically localized entities in both space and time, are constructed from the breathers by a singul...