arXiv subjects

Iva Bačić

Publications and source records attributed to Iva Bačić.

7 recordsLinked to original sources

arXiv2026

A graph theoretic view on small signal stability of inverter-based power grids

Dynamic grid stability is traditionally ensured with synchronous generators. Modern grids rely substantially more on inverter-based resources, which require grid-forming control to guarantee adequate system-wide synchronization and stability. Small-signal stability has granted various centralized and decentralized stability certificates - but these have primarily been limited to sufficient criteria only. In this work, we construct a necessary and sufficient small-signal stability criterion for lossless inverter-based power grids with arbitrary topology. We show that asymptotic stability is equivalent to the positive definiteness of a single matrix that combines network topology, operating point, and effective droop gains. We derive graph-theoretic stability criteria based on an augmented cone graph and show that the contribution of graph cycles is typically small, as illustrated for three IEEE test cases. The resulting framework yields decentralized stability criteria, quantifies the conservatism introduced by decentralization, and may support the development of future grid codes.

eess.SY↗

arXiv2026

Phase locking and multistability in the topological Kuramoto model on cell complexes

Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension within simplicial and cell complexes. We introduce the topological nonlinear Kirchhoff conditions to characterize all phase-locked states of the topological Kuramoto model. These states are organized by winding numbers associated with generalized independent cycles, which quantify how phases wind around these cycles. Using rings, Platonic solids, and regular simplices as illustrative examples, we uncover a universal rule: boundaries must have at least five elements for multistability to arise. We further find that independent winding numbers associated with lower- and higher-dimensional boundaries generate cascades of multistability across dimensions. These results show how the topology and boundary structure of cell complexes influence phase locking and multistability, and provide a general framework for collective dynamics on cell complexes.

nlin.AO↗

arXiv2026

Symmetry breaking in minimum dissipation networks

Both natural and engineered supply networks exhibit universal structural patterns, such as the formation of loops, yet the principles governing optimal structures remain unclear. These patterns can be interpreted as solutions of optimization models, assuming that biological networks evolve toward optimal states and engineered systems are designed accordingly. We study a canonical model of transport networks that minimizes dissipation under a global resource constraint and admits analytical treatment. Symmetry breaking in optimal networks occurs in two distinct forms: weak symmetry breaking, which preserves symmetry in the topology but breaks it in the edge weights, and strong symmetry breaking, which eliminates it entirely. Varying the resource scaling exponent induces discontinuous transitions between these states and the fully symmetric phase, either through bifurcations of local minima or through exchanges of stability between competing optima. Moreover, fluctuations play a nontrivial role: as noise increases, the system can undergo a reentrant transition from strongly symmetry-broken to symmetric and back, implying the existence of an optimal fluctuation level that stabilizes symmetric network structures. These mechanisms persist beyond the minimal model. In a renewable energy network, fluctuations similarly influence optimal topologies. These results establish symmetry breaking as a generic organizing principle of optimal transport networks.

nlin.AO↗

arXiv2024

Impact of physicality on network structure

The emergence of detailed maps of physical networks, like the brain connectome, vascular networks, or composite networks in metamaterials, whose nodes and links are physical entities, have demonstrated the limits of the current network science toolset. Link physicality imposes a non-crossing condition that affects both the evolution and the structure of a network, in a way that the adjacency matrix alone -- the starting point of all graph-based approaches -- cannot capture. Here, we introduce a meta-graph that helps us discover an exact mapping between linear physical networks and independent sets, a central concept in graph theory. The mapping allows us to analytically derive both the onset of physical effects and the emergence of a jamming transition, and show that physicality impacts the network structure even when the total volume of the links is negligible. Finally, we construct the meta-graphs of several real physical networks, which allows us to predict functional features, such as synapse formation in the brain connectome, that agree with empirical data. Overall, our results show that, in order to understand the evolution and behavior of real complex networks, the role of physicality must be fully quantified.

cond-mat.stat-mech↗

arXiv2020

Two paradigmatic scenarios for inverse stochastic resonance

Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for inverse stochastic resonance by considering a paradigmatic model of two adaptively coupled stochastic active rotators whose local dynamics is close to a bifurcation threshold. In the first scenario, shown for the two rotators in the excitable regime, inverse stochastic resonance emerges due to a biased switching between the oscillatory and the quasi-stationary metastable states derived from the attractors of the noiseless system. In the second scenario, illustrated for the rotators in the oscillatory regime, inverse stochastic resonance arises due to a trapping effect associated with a noise-enhanced stability of an unstable fixed point. The details of the mechanisms behind the resonant effect are explained in terms of slow-fast analysis of the corresponding noiseless systems.

nlin.AO↗

arXiv2020

Dynamics of a stochastic excitable system with slowly adapting feedback

We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance, or effectively control the features of the stochastic bursting. The setup can be considered as a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noise-induced fluctuations by a corresponding stationary Fokker-Planck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noise-induced switching between a stationary and an oscillatory regime gives rise to stochastic bursting.

nlin.AO↗

arXiv2018

Disordered configurations of the Glauber model in two-dimensional networks

We analyze the ordering efficiency and the structure of disordered configurations for the zero-temperature Glauber model on Watts-Strogatz networks obtained by rewiring 2D regular square lattices. In the small-world regime, the dynamics fails to reach the ordered state in the thermodynamic limit. Due to interplay of the perturbed regular topology and the energy neutral stochastic state transitions, the stationary state consists of two intertwined domains, manifested as multi-clustered states on the original lattice. Moreover, for intermediate rewiring probabilities, one finds an additional source of disorder due to the low connectivity degree, which gives rise to small isolated droplets of spins. We also examine the ordering process in paradigmatic two-layer networks with heterogeneous rewiring probabilities. Comparing the cases of a multiplex network and the corresponding network with random inter-layer connectivity, we demonstrate that the character of the final state qualitatively depends on the type of inter-layer connections.

cond-mat.stat-mech↗