What does this research mean for the field?

Any negative periodic perturbation of the equilibrium dynamics generator in non-local convolution operators shifts the spectrum to the left half-plane, leading to population extinction in any dimension. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To analyze the spectral properties of non-local convolution-type operators subject to negative periodic perturbations representing increased mortality in spatial population dynamics.

August 24, 2026Markov Processes And Related FieldsOpen Access

Negative Spectrum of Non-local Operators with Periodic Potential

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Authors

СПС. ПироговNational Research University Higher School of Economics EZE. ZhizhinaMoscow Institute of Physics and Technology

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Implication

Theoretical analysis demonstrates negative periodic perturbations shift operator spectra to the left half-plane in continuous spaces, indicating inevitable population extinction across dimensions.

Key Points

To analyze the spectral properties of non-local convolution-type operators subject to negative periodic perturbations representing increased mortality in spatial population dynamics.
Performed spectral analysis on non-local operators of convolution type that govern the evolution of the first correlation function in stochastic birth-and-death dynamics.
Modeled birth kernels incorporating non-symmetric and spatially heterogeneous properties under periodic suppression forces.
Proved that any negative periodic perturbation of the equilibrium dynamics generator shifts the operator spectrum strictly into the left half-plane.
Demonstrated that introducing periodic increases in mortality leads inevitably to total population extinction across all spatial dimensions.

Cite This Study

Пирогов et al. (2026) studied this question.

synapsesocial.com/papers/6a8c0010bca056c88e6deee2 https://doi.org/10.61102/1024-2953-mprf.2026.32.2.003

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Implication

Theoretical analysis demonstrates negative periodic perturbations shift operator spectra to the left half-plane in continuous spaces, indicating inevitable population extinction across dimensions.

Negative Spectrum of Non-local Operators with Periodic Potential

Discussion

Member takes

Implication

Key Points

Cite This Study

Negative Spectrum of Non-local Operators with Periodic Potential

Discussion

Member takes

Implication

Key Points

Cite This Study

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