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Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
Steering of attractors in multistable systems is used to increase the available parameter domains which lead to stable dynamics in nonlinear physical systems, reducing substantially undesirable effects of parametric inaccuracy and noise.…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
The classical stability margin analysis based on the linearized model is widely used in practice even in nonlinear systems. Although linear analysis techniques are relatively standard and have simple implementation structures, they are…
This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of parameter values. More precisely, for a given subset of the parameter space, we develop an algorithm that is capable of…
A non-${\cal{PT}}$-symmetric Hamiltonian system of a Duffing oscillator coupled to an anti-damped oscillator with a variable angular frequency is shown to admit periodic solutions. The result implies that ${\cal{PT}}$-symmetry of a…
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…
This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
In this paper we aim to apply an adaptation of the recently developed technique of sparse identification of nonlinear dynamical systems on a Duffing experimental setup with cubic feedback of the output. The Duffing oscillator described by…
We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the a priori…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…