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We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper…
In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a stable fixed point of a piecewise-smooth map collides with a…
Deterministically controllable multi-state polarizations in ferroelectric materials are promising for the application of next-generation non-volatile multi-state memory devices. However, the achievement of multi-state polarizations has been…
The rational tailoring of transition metal complexes is necessary to address outstanding challenges in energy utilization and storage. Heterobimetallic transition metal complexes that exhibit metal-metal bonding in stacked "double decker"…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
Enzymes are nano-scale machines that have evolved to drive chemical reactions out of equilibrium in the right place at the right time. Given the complexity and specificity of enzymatic function, bottom-up design of enzymes presents a…
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a line of equilibria with an exchange point of normal…
Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic…
We present a simple model system with four hard disks moving in a circular region for which free energy landscapes can be directly calculated and visualized in two and three dimensions. We construct several energy landscapes for our system…
The design of desired behaviors in mechanical metamaterials has produced remarkable advances but has generally neglected two aspects - the inevitable presence of undesired behaviors and the role of dynamics in avoiding such behaviors.…
This work provides a geometric approach to the study of bifurcation and rate induced transitions in a class of non-autonomous systems referred to herein as $\textit{asymptotically slow-fast systems}$, which may be viewed as 'intermediate'…
Collaborative robots must simultaneously be safe enough to operate in close proximity to human operators and powerful enough to assist users in industrial tasks such as lifting heavy equipment. The requirement for safety necessitates that…
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…
We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…
This paper investigates the nonlinear dynamics and phase transitions in power packet network connected with routers, conceptualized as macroscopic information-ratchets. In the emerging paradigm of cyber-physical energy systems, the…
Novel algorithm for designing values of technological parameters for production of Soft Magnetic Composites (SMC) has been created. These parameters are the following magnitudes: hardening temperature $T$ and compaction pressure $p$. They…
Systems with many stable configurations abound in nature, both in living and inanimate matter. Their inherent nonlinearity and sensitivity to small perturbations make them challenging to study, particularly in the presence of external…
Microtransit offers opportunities to enhance urban mobility by combining the reliability of public transit and the flexibility of ride-sharing. This paper optimizes the design and operations of a deviated fixed-route microtransit system…