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Autocatalytic chemical reaction networks are dynamical systems whose linearization around zero, dX/dt = AX, is represented by a Perron-Frobenius matrix A with positive Lyapunov exponent; this exponent gives the growth rate of the species…
Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Recently, Blokhuis et al. gave a stoechiometric definition of autocatalysis for reaction networks, stating the existence of a combination of reactions…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…
Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the…
The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
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…
A Markov chain model for spatially distributed autocatalytic systems with a quadratic reaction rate is considered. An approximate solution for the local probability distribution is obtained in the form of a perturbation expansion for the…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Autocatalysis was recently defined stoichiometrically for reaction networks; five types of minimal autocatalytic networks, termed autocatalytic cores were…
Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…
We introduce the Lyapunov approach to optimal control problems of average risk-sensitive Markov control processes with general risk maps. Motivated by applications in particular to behavioral economics, we consider possibly non-convex risk…
We address the problem of Lyapunov function construction for a class of continuous-time Markov chains with affine transition rates, typically encountered in stochastic chemical kinetics. Following an optimization approach, we take advantage…
Here, we study the ultimately bounded stability of network of mismatched systems using Lyapunov direct method. We derive an upper bound on the norm of the error of network states from its average states, which it achieves in finite time.…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…