Related papers: An Optimization Algorithm for Finding Parameters f…
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…
Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
Many biological systems, such as metabolic pathways, exhibit bistability behavior: these biological systems exhibit two distinct stable states with switching between the two stable states controlled by certain conditions. Since…
We study an ancient problem that in a static or dynamical system, sought an optimal path, which the context always means within an extremal condition. In fact, through those discussions about this theme, we established a universal essential…
We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general, nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however,…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
This article presents a multi-robot trajectory planning method which not only guarantees optimization feasibility and but also resolves deadlocks in obstacle-dense environments. The method is proposed via formulating a recursive…
In this paper we describe a combined combinatorial/numerical approach to studying equilibria and bifurcations in network models arising in Systems Biology. ODE models of the dynamics suffer from high dimensional parameters which presents a…
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…
Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space…
Models in systems biology are mathematical descriptions of biological processes that are used to answer questions and gain a better understanding of biological phenomena. Dynamic models represent the network through rates of the production…