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Species-rich communities, such as the microbiota or microbial ecosystems, provide key functions for human health and climatic resilience. Increasing effort is being dedicated to design experimental protocols for selecting community-level…
Mutualistic networks are formed when the interactions between two classes of species are mutually beneficial. They are important examples of cooperation shaped by evolution. Mutualism between animals and plants plays a key role in the…
A prominent hypothesis in neuroscience proposes that brains achieve optimal performance by operating near a critical point. However, this framework, which often assumes a universal critical point, fails to account for the extensive…
We study the interplay among disorder, RKKY and Kondo interactions in {\it f}-electron alloys. We argue that the non-Fermi liquid behavior observed in these systems is due to the existence of a Griffiths phase close to a quantum critical…
We study dynamical phase transitions in systems with long-range interactions, using the Hamiltonian Mean Field (HMF) model as a simple example. These systems generically undergo a violent relaxation to a quasi-stationary state (QSS) before…
The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species towards rarity or abundance is crucial to assessing ecosystem resilience and…
The dynamics of competing opinions in social network play an important role in society, with many applications in diverse social contexts as consensus, elections, morality and so on. Here we study a model of interacting agents connected in…
Complex system stability can be studied via linear stability analysis using Random Matrix Theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here…
Mutualistic interactions, where individuals from different species can benefit from each other, are widespread across ecosystems. This study develops a general deterministic model of mutualism involving two populations, assuming that…
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation…
Winner-take-all (WTA)--type selection is a fundamental mechanism in networked competition, yet its dependence on higher-order interactions remains insufficiently understood. We study a Lotka--Volterra competitive dynamics on higher-order…
Building on the line of work [DIRT15a], [DIRT15b], [NS17a], [DT17], [HLS18], [HS18] we continue the study of particle systems with singular interaction through hitting times. In contrast to the previous research, we (i) consider very…
A dynamic concordia discors, a finely tuned equilibrium between opposing forces, is hypothesized to drive historical transformations. Similarly, a precise interplay of excitation and inhibition, often approximated by an 80:20 ratio,…
Species coexistence is a complex, multifaceted problem. At an equilibrium, coexistence requires two conditions: stability under small perturbations; and feasibility, meaning all species abundances are positive. Which of these two conditions…
Diverse communities of competing species are generally characterized by substantial niche overlap and strongly stochastic dynamics. Abundance fluctuations are proportional to population size, so the dynamics of rare populations is slower.…
The effect of quenched disorder on the low-energy properties of various antiferromagnetic spin ladder models is studied by a numerical strong disorder renormalization group method and by density matrix renormalization. For strong enough…
We investigate the nonequilibrium phase transition in the disordered contact process in the presence of long-range spatial disorder correlations. These correlations greatly increase the probability for finding rare regions that are locally…
We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we…
We study the dynamics of a ring of patches with vegetation-prey-predator populations, coupled through interactions of the Lotka-Volterra type. We find that the system yields aperiodic, recurrent and rare explosive bursts of predator density…
Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions…