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How a responsive reproduction factor is determinant in a prey-predator dynamics: A numerical and analytical study in a discrete-time model.
Chaos
January 2025
Physics Institute, University of São Paulo, 05508-090 São Paulo, SP, Brazil.
In this work, we investigate the dynamics of a discrete-time prey-predator model considering a prey reproductive response as a function of the predation risk, with the prey population growth factor governed by two parameters. The system can evolve toward scenarios of mutual or only of predators extinction, or species coexistence. We analytically show all different types of equilibrium points depending on the ranges of growth parameters.
View Article and Find Full Text PDFBifurcations of phase portraits and chaotic behaviors of the (2+1)-dimensional double-chain DNA system with beta derivative: A qualitative approach.
Heliyon
July 2024
Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj 8100, Bangladesh.
Qualitative analysis in mathematical modeling has become an important research area within the broad domain of nonlinear sciences. In the realm of qualitative analysis, the bifurcation method is one of the significant approaches for studying the structure of orbits in nonlinear dynamical systems. To apply the bifurcation method to the (2 + 1)-dimensional double-chain Deoxyribonucleic Acid system with beta derivative, the bifurcations of phase portraits and chaotic behaviors, combined with sensitivity and multi-stability analysis of this system, are examined.
View Article and Find Full Text PDFQuasiperiodic shrimp-shaped domains in intrinsically coupled oscillators.
Chaos
December 2024
Institute of Physics, University of São Paulo, 05508-900 São Paulo, SP, Brazil.
Article Synopsis
- The study explores the formation of intricate patterns, or "metamorphic tongues," in a system made up of a rotor and a Duffing oscillator, highlighting their unusual quasiperiodic and chaotic behaviors.
- Researchers use Lyapunov exponents to map out self-similar islands of stability and chaos in the system's two-dimensional parameter space.
- Notably, quasiperiodic shrimp-shaped domains exhibit features akin to periodic systems, including complicated behaviors like torus-doubling and torus-tripling.
Shearless and periodic attractors in the dissipative Labyrinthic map.
Chaos
December 2024
Institute of Physics, University of São Paulo, São Paulo 13506-900, SP, Brazil.
The Labyrinthic map is a two-dimensional area-preserving map that features a robust transport barrier known as the shearless curve. In this study, we explore a dissipative version of this map, examining how dissipation affects the shearless curve and leads to the emergence of quasi-periodic or chaotic attractors, referred to as shearless attractors. We present a route to chaos of the shearless attractor known as the Curry-Yorke route.
View Article and Find Full Text PDFArnold tongues, shrimp structures, multistability, and ecological paradoxes in a discrete-time predator-prey system.
Chaos
December 2024
Department of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, Madhya Pradesh, India.
This paper explores a discrete-time system derived from the well-known continuous-time Rosenzweig-MacArthur model using the piecewise constant argument. Examining the impact of increasing carrying capacity and harvesting efforts, we uncover intricate phenomena, such as periodicity, quasiperiodicity, period-doubling, period-bubbling, and chaos. Our analysis reveals that increasing the carrying capacity of prey species can lead to both system stabilization and destabilization.
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