<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Population dynamics has a wide range of applications in ecological theory, especially in the fields of plant and animal conservation and the management and development of ecological environments. Periodic solution analysis of a population dynamics model for pulsating organisms. The influence of impulsive dynamics on the periodic solution of the system is investigated in this paper, which considers several types of population dynamics systems with impulsive effects. First, the impulsive differential modeling of the model of a constantator in a polluted environment considering time-lagged growth response and impulsive inputs proves that only ̄<italic>t</italic> needs to be sufficiently large to have <italic>x</italic>(<italic>t</italic>) > <italic>m</italic><sub>x</sub>, such that, the constantator seeks a unique periodic solution for microbial extinction and persistent survivability. Next, a model of integrated pest control is modeled to find, a periodic solution for pest extinction and the existence of (0, <italic>I</italic>* (<italic>t</italic>)) is globally stable. Then, a Lur’e system with impulsive biodynamics is explored, modeled with uncertain parameters, and simulated with Chua’s circuit system to determine that the state trajectory lines all eventually converge to 0 and have stable periodic solutions. Finally, the Beddington-DeAngelis predator-prey model with impulsive effects is used to argue, using correlation priming, for the existence of 
<inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns-2024-0298_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>z</mi></mrow> <mi>i</mi><mo>*</mo></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mo>exp</mo><mrow><mo>{</mo> <mrow><msubsup><mrow><mi>x</mi></mrow> <mi>i</mi><mo>*</mo></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow> <mo>}</mo></mrow></mrow></math>
<tex-math>z_i^*\left( t \right) = \exp \left\{ {x_i^*\left( t \right)} \right\}</tex-math>
</alternatives>
</inline-formula>, <italic>i</italic> = 1, 2, such that <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns-2024-0298_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>z</mi></mrow><mo>*</mo></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mrow><mrow><mo>(</mo><mrow><msubsup><mrow><mi>z</mi></mrow> <mn>1</mn><mo>*</mo></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi> </mi><msubsup><mrow><mi>z</mi></mrow><mn>2</mn><mo>*</mo></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mi>T</mi></msup></mrow></math>
<tex-math>{z^*}\left( t \right) = {\left( {z_1^*\left( t \right),\,z_2^*\left( t \right)} \right)^T}</tex-math>
</alternatives>
</inline-formula> there is a positive <italic>ω</italic> − periodic solution for this system.</p>
</abstract>

Population dynamics has a wide range of applications in ecological theory, especially in the fields of plant and animal conservation and the management and development of ecological environments. Periodic solution analysis of a population dynamics model for pulsating organisms. The influence of impulsive dynamics on the periodic solution of the system is investigated in this paper, which considers several types of population dynamics systems with impulsive effects. First, the impulsive differential modeling of the model of a constantator in a polluted environment considering time-lagged growth response and impulsive inputs proves that only ̄t needs to be sufficiently large to have x(t) > mx, such that, the constantator seeks a unique periodic solution for microbial extinction and persistent survivability. Next, a model of integrated pest control is modeled to find, a periodic solution for pest extinction and the existence of (0, I* (t)) is globally stable. Then, a Lur’e system with impulsive biodynamics is explored, modeled with uncertain parameters, and simulated with Chua’s circuit system to determine that the state trajectory lines all eventually converge to 0 and have stable periodic solutions. Finally, the Beddington-DeAngelis predator-prey model with impulsive effects is used to argue, using correlation priming, for the existence of 



z i*(t)=exp{ x i*(t) }
z_i^*\left( t \right) = \exp \left\{ {x_i^*\left( t \right)} \right\}

, i = 1, 2, such that 


z*(t)=(z 1*(t), z2*(t))T
{z^*}\left( t \right) = {\left( {z_1^*\left( t \right),\,z_2^*\left( t \right)} \right)^T}

 there is a positive ω − periodic solution for this system.

Periodic solution analysis of a population dynamics system model for pulsating organisms

Zhengzhou Technology and Business University

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Population dynamics has a wide range of applications in ecological theory, especially in the fields of plant and animal conservation and the management and...

Periodic solution analysis of a population dynamics system model for pulsating organisms

Published Online: Jan 31, 2024

Page range: -

Received: Dec 26, 2023

Accepted: Jan 02, 2024

DOI: https://doi.org/10.2478/amns-2024-0298

Keywords
Population dynamics, Impulsive differential equations, Constantizer model, Lur’e system, Periodic solutions

© 2024 Mingyin Du, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Periodic solution analysis of a population dynamics system model for pulsating organisms

Published Online: Jan 31, 2024

Page range: -

Received: Dec 26, 2023

Accepted: Jan 02, 2024

DOI: https://doi.org/10.2478/amns-2024-0298

KeywordsPopulation dynamics, Impulsive differential equations, Constantizer model, Lur’e system, Periodic solutions

© 2024 Mingyin Du, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Population dynamics, Impulsive differential equations, Constantizer model, Lur’e system, Periodic solutions