Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.29725

Higher-Order Competition as a Minimal Mechanism for Spatial Pattern Diversity in Population Dynamics

David Pinto-Ramos·Anudeep Surendran·Ricardo Martinez-Garcia
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that negative feedback alone generates the diversity of self-organized shapes usually attributed to scale-dependent activation-inhibition. For a broad class of kernels, pairwise competition models only generate hexagonal spot arrays. Higher-order terms eliminate this restriction and promote stripes and gaps. Combining individual-based simulations and nonlinear analysis, we derive the pattern-selection thresholds and construct the full state diagram, including an unusual spots-stripes-spots sequence. Spot patterns are thus not a reliable indicator of proximity to a tipping point.

Explore related subjects

nlin.AOphysics.bio-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

David Pinto-Ramos, Anudeep Surendran, Ricardo Martinez-Garcia. 2026-09-24. Higher-Order Competition as a Minimal Mechanism for Spatial Pattern Diversity in Population Dynamics. https://arxiv.org/abs/2609.29725

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

From Periodicity to Chaos - Stabilization, Bifurcation, and Synchronization of the Van der Pol Oscillator

This work investigates the dynamics of the van der Pol oscillator, a well-known dynamical model used to represent many naturally occurring phenomena, under both unforced and externally forced conditions, with a focus on its stability characteristics and bifurcation behavior. An approximate analytical solution is derived using the Method of Multiple Scales (MMS) and validated against numerical simulations conducted via the ode45 solver. The evolution of the system's limit cycle is examined as the strength of the nonlinear damping term increased. A range of bifurcation scenarios is explored by systematically varying relevant control parameters. The system's response to external forcing at different damping levels is analyzed to uncover transitions toward chaotic behavior and subsequent phase locking (entrainment). Finally, the relevance of the van der Pol oscillator as a model for naturally occurring rhythmic or periodic processes is discussed, highlighting its applicability in representing biological and physical systems.

nlin.AO↗
arXiv2026

Frequency bursts in adaptive delay-coupled oscillators

We report on frequency bursting oscillations in a system of phase oscillators with adaptive and delayed coupling. Adaptation of the coupling strengths is considered slow and depends on the phase shift between the oscillators. We find due to the combined chain of adaptation, collective dynamics, and time delays, the system robustly achieves a state in which the oscillator's frequencies are nearly synchronized but detuned by an integer number of small adaptation frequencies. We demonstrate that this quantization of the detuning is caused by alternating slow and fast transitions. Moreover, the observed motions take the form of bursts of instantaneous frequency, and the number of spikes in each burst corresponds to the quantization level of the detuning. We provide a fast-slow analysis of this phenomenon and explain the mechanisms behind the emergence of bursts. Our findings indicate that these frequency bursting oscillations are robust and exist stably within finite parameter regions.

nlin.AO↗
arXiv2026

Discrete-time Kuramoto model with phase lag: Linear stability analysis and onset of synchronization

We investigate the discrete-time version of the Kuramoto model with phase lag, which comprises globally-coupled phase oscillators of distributed frequencies that are evolving under a nonlinear map. In the continuum limit of an infinite number of oscillators ($N\to \infty$), we derive the exact Frobenius-Perron equation for the time evolution of the single-oscillator probability density, and study linear stability of the incoherent state. Instability signals onset of synchronization. The corresponding synchronization threshold is obtained analytically for the case of a Lorentzian distribution of the oscillator frequencies. The threshold differs from that of the continuous-time Kuramoto model, reflecting the fundamentally different stability conditions for discrete-time maps and continuous-time flows. Beyond synchronization threshold, we observe several interesting nonlinear phenomena: Unlike the classical Kuramoto model, the discrete-time version exhibits periodic and chaotic states. Numerical simulations of the finite-$N$ system confirm the analytical prediction for the synchronization threshold, while highlighting breakdown of the celebrated Ott-Antonsen ansatz invoked to conveniently study the continuous-time Kuramoto model in terms of a low-dimensional description.

nlin.AO↗