4.5 Article

Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems

Related references

Note: Only part of the references are listed.
Article Physics, Multidisciplinary

Counting equilibria in a random non-gradient dynamics with heterogeneous relaxation rates

Bertrand Lacroix-A-Chez-Toine et al.

Summary: We study a nonlinear autonomous random dynamical system with Gaussian random interactions. By computing the average modulus of the determinant of the random Jacobian matrix, we obtain the annealed complexities of stable equilibria and all types of equilibria. For short-range correlated coupling fields, we derive exact analytical results for the complexities in the large system limit, extending previous results for homogeneous relaxation spectrum. We find a "topology trivialisation" transition from a complex phase with exponentially many equilibria to a simple phase with a single equilibrium as the magnitude of the random field decreases. Within the complex phase, the complexity of stable equilibria undergoes an additional transition from a phase with exponentially small probability of finding a single stable equilibrium to a phase with exponentially many stable equilibria as the fraction of gradient component of the field increases. The behavior of the complexity at the transition is conjectured to be universal, depending only on the small lambda behavior of the relaxation rate spectrum. We also provide insights into a counting problem related to wave scattering in a disordered nonlinear medium.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2022)

Article Biochemistry & Molecular Biology

Instabilities of complex fluids with partially structured and partially random interactions

Giorgio Carugno et al.

Summary: This theory model explores thermodynamic instabilities of complex fluids consisting of interacting chemical species organized in families, with family condensation, family demixing, and random demixing as three types of fluid instabilities. The critical spinodal density of these instabilities is determined, showing finite values for family condensation and family demixing, while increasing as the square root of the number of species for random demixing. The developed framework is used to describe phase-separation instability of the cytoplasm induced by a change in pH.

PHYSICAL BIOLOGY (2022)

Article Physics, Multidisciplinary

Delocalization transition in low energy excitation modes of vector spin glasses

Silvio Franz et al.

Summary: In this study, we investigate the energy minima of a fully-connected m-components vector spin glass model in an external magnetic field, and study the transition from paramagnetic phase to spin glass phase. The spectral properties of the model are examined and it is found that the spectrum is gapless with pseudo-gap. Despite the long-range nature of the model, the eigenstates close to the edge of the spectrum display quasi-localization properties.

SCIPOST PHYSICS (2022)

Article Physics, Multidisciplinary

Effects of intraspecific cooperative interactions in large ecosystems

Ada Altieri et al.

Summary: We analyze the role of the Allee effect in ecological communities formed by a large number of species using the generalized Lotka-Volterra model. Our findings highlight the significant role played by the functional response in determining aggregate behaviors of large ecosystems.

SCIPOST PHYSICS (2022)

Article Physics, Fluids & Plasmas

Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

Andrea Marcello Mambuca et al.

Summary: This study analyzes the stability of linear dynamical systems defined on sparse, random graphs. The results reveal that the nature of local interactions has a strong influence on system stability. Interestingly, antagonistic systems that only contain predator-prey interactions can be stable under certain conditions and exhibit peculiar oscillatory behavior under specific mean degree. Additionally, a dynamical phase transition and critical mean degree are found in antagonistic systems.

PHYSICAL REVIEW E (2022)

Article Mathematics, Applied

POSITIVE SOLUTIONS FOR LARGE RANDOM LINEAR SYSTEMS

Pierre Bizeul et al.

Summary: The study investigates the positivity of solutions in a large linear system and its relationship with the scaling factor, revealing a sharp phase transition at a specific threshold and providing a method to evaluate the probability of positivity. These linear systems are commonly found in LV differential equations describing interactions in biological communities, offering a stability criterion for such systems.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2021)

Article Multidisciplinary Sciences

Exploring the effect of network topology, mRNA and protein dynamics on gene regulatory network stability

Yipei Guo et al.

Summary: Maintaining stable protein concentrations in cells is crucial for proper cellular functioning, with network topology playing a key role in ensuring stability constraints and shaping evolutionary processes.

NATURE COMMUNICATIONS (2021)

Article Mechanics

Stability of large complex systems with heterogeneous relaxation dynamics

Pierre Mergny et al.

Summary: In this study, the probability of stability of a large complex system within the framework of a generalized May model is investigated, focusing on the impact of inhomogeneities in intrinsic damping rates on system stability. It is found that as the interaction strength increases, the system undergoes a phase transition from a stable phase to an unstable phase.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2021)

Article Physics, Multidisciplinary

Localization and Universality of Eigenvectors in Directed Random Graphs

Fernando Lucas Metz et al.

Summary: The study presents a general theory for the statistics of right eigenvector components in directed random graphs. It shows that the localization transition critical mean degree is independent of degree fluctuations, and the distribution of right eigenvector components is solely determined by the degree distribution in the high connectivity limit.

PHYSICAL REVIEW LETTERS (2021)

Article Physics, Fluids & Plasmas

Nonlinearity-generated resilience in large complex systems

S. Belga Fedeli et al.

Summary: The study found that as long as the origin remains stable, the system will be surrounded by a resilience gap with no other fixed points within a radius r(*) > 0. When the origin loses local stability, the radius r(*) disappears, leading to the system becoming less resilient.

PHYSICAL REVIEW E (2021)

Article Multidisciplinary Sciences

Dispersal-induced instability in complex ecosystems

Joseph W. Baron et al.

NATURE COMMUNICATIONS (2020)

Article Physics, Multidisciplinary

Spectral density of dense random networks and the breakdown of the Wigner semicircle law

Fernando L. Metz et al.

PHYSICAL REVIEW RESEARCH (2020)

Article Physics, Multidisciplinary

Linear stability analysis of large dynamical systems on random directed graphs

Izaak Neri et al.

PHYSICAL REVIEW RESEARCH (2020)

Article Physics, Multidisciplinary

Universal transient behavior in large dynamical systems on networks

Wojciech Tarnowski et al.

PHYSICAL REVIEW RESEARCH (2020)

Article Physics, Multidisciplinary

Spectral theory of sparse non-Hermitian random matrices

Fernando Lucas Metz et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2019)

Article Physics, Multidisciplinary

Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka?Volterra model of ecosystems

F. Roy et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2019)

Article Statistics & Probability

The Circular Law for random regular digraphs

Nicholas A. Cook

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES (2019)

Article Physics, Multidisciplinary

Marginally stable equilibria in critical ecosystems

Giulio Biroli et al.

NEW JOURNAL OF PHYSICS (2018)

Article Statistics & Probability

Non-Hermitian random matrices with a variance profile (I): deterministic equivalents and limiting ESDs

Nicholas Cook et al.

ELECTRONIC JOURNAL OF PROBABILITY (2018)

Article Physics, Fluids & Plasmas

Effect of population abundances on the stability of large random ecosystems

Theo Gibbs et al.

PHYSICAL REVIEW E (2018)

Review Physics, Multidisciplinary

Cleaning large correlation matrices: Tools from Random Matrix Theory

Joel Bun et al.

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS (2017)

Article Ecology

Self-regulation and the stability of large ecological networks

Gyorgy Barabas et al.

NATURE ECOLOGY & EVOLUTION (2017)

Article Statistics & Probability

Extremal eigenvalues and eigenvectors of deformed Wigner matrices

Ji Oon Lee et al.

PROBABILITY THEORY AND RELATED FIELDS (2016)

Article Physics, Multidisciplinary

Random antagonistic matrices

Giovanni M. Cicuta et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2016)

Article Physics, Multidisciplinary

Eigenvalue Outliers of Non-Hermitian Random Matrices with a Local Tree Structure

Izaak Neri et al.

PHYSICAL REVIEW LETTERS (2016)

Article Multidisciplinary Sciences

Nonlinear analogue of the May-Wigner instability transition

Yan V. Fyodorov et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2016)

Article Multidisciplinary Sciences

No complexity-stability relationship in empirical ecosystems

Claire Jacquet et al.

NATURE COMMUNICATIONS (2016)

Article Physics, Fluids & Plasmas

Properties of networks with partially structured and partially random connectivity

Yashar Ahmadian et al.

PHYSICAL REVIEW E (2015)

Article Physics, Multidisciplinary

Transition to Chaos in Random Neuronal Networks

Jonathan Kadmon et al.

PHYSICAL REVIEW X (2015)

Article Statistics & Probability

Low rank perturbations of large elliptic random matrices

Sean O'Rourke et al.

ELECTRONIC JOURNAL OF PROBABILITY (2014)

Article Statistics & Probability

Outliers in the spectrum of iid matrices with bounded rank perturbations

Terence Tao

PROBABILITY THEORY AND RELATED FIELDS (2013)

Article Statistics & Probability

UNIVERSALITY AND THE CIRCULAR LAW FOR SPARSE RANDOM MATRICES

Philip Matchett Wood

ANNALS OF APPLIED PROBABILITY (2012)

Article Multidisciplinary Sciences

Stability criteria for complex ecosystems

Stefano Allesina et al.

NATURE (2012)

Article Multidisciplinary Sciences

Diversity of Interaction Types and Ecological Community Stability

A. Mougi et al.

SCIENCE (2012)

Article Statistics & Probability

Around the circular law

Charles Bordenave et al.

PROBABILITY SURVEYS (2012)

Article Physics, Fluids & Plasmas

Cavity approach to the spectral density of non-Hermitian sparse matrices

Tim Rogers et al.

PHYSICAL REVIEW E (2009)

Article Multidisciplinary Sciences

Stability in real food webs: Weak links in long loops

AM Neutel et al.

SCIENCE (2002)