Modeling and analysis of demand-supply dynamics with a collectability factor using delay differential equations in economic growth via the Caputo operator

Qiliang Chen; Dipesh; Pankaj Kumar; Haci Mehmet Baskonus; Qiliang Chen; Dipesh; Pankaj Kumar; Haci Mehmet Baskonus

doi:10.3934/math.2024362

AIMS Mathematics

2024, Volume 9, Issue 3: 7471-7191. doi: 10.3934/math.2024362

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Modeling and analysis of demand-supply dynamics with a collectability factor using delay differential equations in economic growth via the Caputo operator

1.
School of Economics and Finance, Chongqing University of Technology, Chongqing, China
2.
Department of Mathematics, Lovely Professional University, Phagwara- 144411, India
3.
Department of Mathematics and Science Education, Faculty of Education, Harran University, Şanlıurfa, Türkiye

Received: 28 December 2024 Revised: 05 February 2024 Accepted: 08 February 2024 Published: 21 February 2024
MSC : 34Axx, 34Dxx, 34Fxx

In this paper, to investigate the dynamic interplay between supply and demand, with a focus on collectability, a novel mathematical model was introduced via conformable operator. This model considers the possibility that operating expenses or a lack of raw materials causes a manufacturing delay than the supply of goods instantly matching demand. This maturation (delay) is represented by the delay factor $ \left(\tau \right) $. Stability analysis revolves around the equilibrium point other than zero. Chaotic behavior emerges through Hopf bifurcation at the critical delay parameter value. If this delay parameter is even slightly perturbed, oscillatory limit cycles can be induced in the market dynamics, leading to equilibrium with brisk market expansion, frequent recessions, and sudden collapses. We conducted sensitivity and directional analysis on a number of factors while also examining the stability and duration of the Hopf bifurcation. Numerical findings were validated using MATLAB. Additionally, the Caputo operator was used to examine the fractional of demand and supply dynamics. Importantly, we assumed a pivotal role in advancing fair labor practices and fostering economic growth on a national scale.
- production,
- demand,
- apply stability,
- delay,
- Hopf bifurcation,
- Caputo
Citation: Qiliang Chen, Dipesh, Pankaj Kumar, Haci Mehmet Baskonus. Modeling and analysis of demand-supply dynamics with a collectability factor using delay differential equations in economic growth via the Caputo operator[J]. AIMS Mathematics, 2024, 9(3): 7471-7191. doi: 10.3934/math.2024362

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Abstract

In this paper, to investigate the dynamic interplay between supply and demand, with a focus on collectability, a novel mathematical model was introduced via conformable operator. This model considers the possibility that operating expenses or a lack of raw materials causes a manufacturing delay than the supply of goods instantly matching demand. This maturation (delay) is represented by the delay factor $ \left(\tau \right) $. Stability analysis revolves around the equilibrium point other than zero. Chaotic behavior emerges through Hopf bifurcation at the critical delay parameter value. If this delay parameter is even slightly perturbed, oscillatory limit cycles can be induced in the market dynamics, leading to equilibrium with brisk market expansion, frequent recessions, and sudden collapses. We conducted sensitivity and directional analysis on a number of factors while also examining the stability and duration of the Hopf bifurcation. Numerical findings were validated using MATLAB. Additionally, the Caputo operator was used to examine the fractional of demand and supply dynamics. Importantly, we assumed a pivotal role in advancing fair labor practices and fostering economic growth on a national scale.

References

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