Theoretical Physics: Complex Systems

• Aging of dynamic systems: We are interested in artificial and natural systems, for which we distinguish two types of dynamic processes: production processes that require high-precision manufacturing, and the repair processes needed to maintain this precision and thus guarantee the quality or functioning of products. The challenging question is whether error accumulation can be avoided and if so, under what conditions if a finite amount of resources is accessible in a finite interval of time. Inspired from biological experiments, the costs are assumed to diverge for perfect precision, thus, errors are inherent to both production and repair processes. If errors accumulate beyond a tolerable threshold in the course of time, we term this accumulation process “aging of the dynamic system”. 
• Criticality in dynamical systems: Criticality is assumed to be one of the important organization principles of living organisms. It includes, for example, high sensitivity to perturbations, critical slowing down and characteristic scaling behavior. For biological or artificial systems, which perform computations, operating near critical points has functional advantages for information processing. Criticality in brain dynamics is currently a hot topic. We have searched for critical phenomena in heteroclinic dynamics, which researchers use to describe in particular transient cognitive processes. 
• Physical basis of cognitive processes: Cognitive processes in the human brain are transient, but usually exactly reproducible. A fundamental question in neuroscience concerns physical mechanisms that allow dynamics which is transient and reproducible at the same time. We are exploring heteroclinic dynamics as a possible framework, in which signals are forwarded in a well-controlled temporal order. In neuronal systems, we assume that information is encoded both in space and time coordinates, in particular also in the temporal order of spiking neuronal populations. 
• Stability of power grids: Renewable energies account for a larger percentage of power supply than ever before, but wind and solar are intrinsically uncertain and this uncertainty poses challenges for the management and performance of the grid. Nowadays, consumers can also act as producers and feed locally produced power into the distribution grid. In addition, the energy market is becoming increasingly delocalised with less centralized control. In view of these challenges, we developed algorithms which allow a fast estimation of the state of the grid, fast enough to be applicable to large grids. Moreover, we estimate the frequency of rare blackout events to quantify what ‘rare’ means. For the energy market we propose statutory and economic measures to stabilize it.

• We analyzed the conditions under which aging in the sense of error accumulation can be kept below a tolerable threshold. We found that the fate of the system (as to whether this threshold is exceeded or not) depends on the relationship between the costs and the required precision. 
• We identified typical features of critical phenomena at bifurcation points in networks, at which heteroclinic dynamics are ongoing at each site of a spatial grid. 
• We have shown how the information inherent in the temporally ordered neuronal excitation patterns can be processed over space when a few pacemaker cells entrain many other cells to synchronize their oscillations with the pacemakers. Our description realizes in common to brain dynamics: these are processes which are hierarchically organized locally, but ongoing in parallel in different areas of the brain. 
• Our analysis of the volatility of the energy market with tools from statistical mechanics and nonlinear dynamics complements the perspective of economists. It points to collective phenomena such as tipping points. Intuitively, these features are not predictable, neither are they understandable from the mere perspective of economics. understandable from the mere perspective of economics. 
• Prof. Meyer-Ortmanns contributed to two books, one entitled From Electrons to Elephants and Elections, published in 2022, the other one entitled The Energetics of Computing in Life and Machines, published in 2019.

The Statistical Physics/Nonlinear Dynamics group, headed by Prof. Meyer-Ortmanns, comprised one postdoc and two PhD students. Project funders included the BMBF and the DFG.

• M. Voit and H. Meyer-Ortmanns, How aging can be an unavoidable fate of dynamical systems, New J. Phys. (2019). 
• M. Voit and H. Meyer-Ortmanns, Emerging criticality at bifurcation points in heteroclinic dynamics, Phys. Rev. Res. 2. (2020). 
• B. Thakur and H. Meyer-Ortmanns, Heteroclinic units acting as pacemakers: Entrained dynamics for cognitive processes, J. Phys. Complex. (2022). 
• T. Ritmeester and H. Meyer-Ortmanns, The cavity method for minority games between arbitrageurs on financial markets, J. Stat. Mech. (2022). 
• D. Witthaut, F. Hellmann, J. Kurths, S. Kettemann, H. Meyer-Ortmanns, M. Timme, Collective nonlinear dynamics and self-organization in decentralized power grids, Rev. Mod. Phys. (2022).