https://doi.org/10.1140/epjp/s13360-024-05445-z
Regular Article
Investigating the influence of multiplicative noise on available resources: a stochastic production–consumption model incorporating a logistic-like weak Allee effect
1
School of Management Engineering, Zhengzhou University of Aeronautics, 450046, Zhengzhou, Henan, China
2
School of Economics, Zhengzhou University of Aeronautics, 450046, Zhengzhou, Henan, China
Received:
11
May
2024
Accepted:
11
July
2024
Published online:
22
July
2024
To optimize resource utilization and minimize the risk of depletion, this paper proposes a production-consumption model that incorporates a logistic-like weak Allee effect and multiplicative noise. The survivability of the model is first investigated using the theory of random dynamical system, which is determined by a critical parameter 
. Specifically, when 
, the system becomes extinct; however, for 
, it exhibits a unique nontrivial stationary distribution with an explicit density function, thereby indicating the persistence of available resources. Furthermore, comprehensive discussions on dynamical bifurcation and phenomenological bifurcation are provided. Our theoretical results show that the parameter not only serves as a dynamical bifurcation point of the model, but also plays a crucial role in the phenomenological bifurcation by inducing four distinct alterations in the shape of the density function. Specifically, variations in noise levels can induce state transitions within the system, leading to redistribution or even depletion of available resources.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
