Publications

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2023

14.

Figure 13: Isospike diagram of the system (4.1) in 𝑞1 −𝑚 biparametric space ((𝑞1,𝑚) ∈ [1, 12]×[0, 1]). The figure is obtained by integrating the system for 801 × 801

pair of values of (𝑞1,𝑚) with fixed initial condition (0.5, 0.7, 9.0)

An investigation of the parameter space in a tri-trophic food chain model with refuge

Authors: Ruma Kumbhakar, Mainul Hossain, Sarbari Karmakar, & Nikhil Pal

Journal: Mathematics and Computers in Simulation 217: 37-59 (2024).

http://dx.doi.org/10.1016/j.matcom.2023.10.010

BibTeX Citation:

@article{kumbhakar2024investigation,

title={An investigation of the parameter space in a tri-trophic food chain model with refuge},

author={Kumbhakar, Ruma and Hossain, Mainul and Karmakar, Sarbari and Pal, Nikhil},

journal={Mathematics and Computers in Simulation},

volume={217},

pages={37--59},

year={2024},

publisher={Elsevier}

}

13.

Figure 20(b): The enlargement of the black-dashed rectangular box shown in Fig 20 (a), unveils the presence of periodic Arnold tongues spanned in the quasiperiodic zone and also indicates the system’s similar type of dynamics as noticed in earlier cases.

Chaos, periodic structures, and multistability: Complex dynamical behaviors of an eco-epidemiological model in parameter planes

Authors: Shilpa Garai, Mainul Hossain, Sarbari Karmakar, & Nikhil Pal

Journal: Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 8 (2023).

https://doi.org/10.1063/5.0156110

BibTeX Citation:

@article{garai2023chaos,

title={Chaos, periodic structures, and multistability: Complex dynamical behaviors of an eco-epidemiological model in parameter planes},

author={Garai, Shilpa and Hossain, Mainul and Karmakar, Sarbari and Pal, Nikhil},

journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},

volume={33},

number={8},

year={2023},

publisher={AIP Publishing}

}

12.

The isospike diagram of system (2) in the biparametric space of k and b1. The vertical line k=0 separates the region of emigration (k<0) from the region of immigration (k>0). The periodicity of peaks in the time series evolution of system (2) associated with each point in the above biparametric space is indicated by a specific color.

Structure of parameter space of a three-species food chain model with immigration and emigration

Authors: Mainul Hossain, Ruma Kumbhakar, Nikhil Pal, & Jürgen Kurths

Journal: Nonlinear Dynamics (2023): 1-18. https://doi.org/10.1007/s11071-023-08573-w

BibTeX Citation:

@article{hossain2023structure,

title={Structure of parameter space of a three-species food chain model with immigration and emigration},

author={Hossain, Mainul and Kumbhakar, Ruma and Pal, Nikhil and Kurths, J{\"u}rgen},

journal={Nonlinear Dynamics},

pages={1--18},

year={2023},

publisher={Springer}

}

2022

11.

A zoomed view of the isospike and LLE diagram of system (2.2) corresponding to the large white box placed inside Fig. 6a.We have a whole array of shrimp-shaped periodic structures assembled in a symmetric way.

Dynamics in the biparametric spaces of a three-species food chain model with vigilance

Authors: Mainul Hossain, Ruma Kumbhakar & Nikhil Pal

Journal: Chaos, Solitons & Fractals 162 (August, 2022): 112438. https://doi.org/10.1016/j.chaos.2022.112438

BibTeX Citation:

@article{hossain2022dynamics,

title={Dynamics in the biparametric spaces of a three-species food chain model with vigilance},

author={Hossain, Mainul and Kumbhakar, Ruma and Pal, Nikhil},

journal={Chaos, Solitons \& Fractals},

volume={162},

pages={112438},

year={2022},

publisher={Elsevier}

}

10.

Lyapunov exponent diagrams of system (2.2) in the area enclosed by the red-dotted rectangle in Fig. 2. We can see that there are several organized periodic structures in the shape of shrimp that repeat at regular intervals inside the chaotic regime (yellow-green).

Bifurcation, chaos, multistability, and organized structures in a predator-prey model with vigilance

Authors: Mainul Hossain, Shilpa Garai, Sajad Jafari & Nikhil Pal

Journal: Chaos (Woodbury, N.Y.) 32(6):063139. http://dx.doi.org/10.1063/5.0086906

BibTeX Citation:

@article{hossain2022bifurcation,

title={Bifurcation, chaos, multistability, and organized structures in a predator-prey model with vigilance},

author={Hossain, Mainul and Garai, Shilpa and Jafari, Sajad and Pal, Nikhil},

journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},

volume={32},

number={6},

pages={063139},

year={2022},

publisher={AIP Publishing LLC}

}

9.

Figure shows bi-parametric regions of stability (Subfig. 3a) and the variation of densities of all three populations in u−v space

Impact of vigilance on the density variations in a food chain model

Authors: Mainul Hossain, Shilpa Garai, Sarbari Karmakar, Nikhil Pal & Joydev Chattopadhyay

Journal: Ecological Complexity 50:100996 http://dx.doi.org/10.1016/j.ecocom.2022.100996

BibTeX Citation:

@article{hossain2022impact,

title={Impact of vigilance on the density variations in a food chain model},

author={Hossain, Mainul and Garai, Shilpa and Karmakar, Sarbari and Pal, Nikhil and Chattopadhyay, Joydev},

journal={Ecological Complexity},

volume={50},

pages={100996},

year={2022},

publisher={Elsevier}

}

2021

8.

Figure shows dynamics of the system in three different bi-parametric regions. These are obtained using fixed initial condition (x0, y0, z0, p0) =(0.5, 0.9, 11, 0.5). Here, b1 = 3.

Bifurcations and multistability in a food chain model with nanoparticles

Authors: Mainul Hossain, N C Pati, Saheb Pal, Sourav Rana, Nikhil Pal & G C Layek

Journal: Mathematics and Computers in Simulation 190:808–825 http://dx.doi.org/10.1016/j.matcom.2021.06.017

BibTeX Citation:

@article{hossain2021nano,

title={Bifurcations and multistability in a food chain model with nanoparticles},

author={Hossain, Mainul and Pati, NC and Pal, Saheb and Rana, Sourav and Pal, Nikhil and Layek, GC},

journal={Mathematics and Computers in Simulation},

volume={190},

pages={808--825},

year={2021},

publisher={Elsevier}

}

7.

Figure shows self-similar patterns in different zoomed-in versions of the basin of attraction presented in Fig. 15(b) corresponding to (θ, k) = (0.4, 0.0453).

Bifurcations, chaos, and multistability in a nonautonomous predator-prey model with fear

Authors: Mainul Hossain, Saheb Pal, Pankaj Kumar Tiwari & Nikhil Pal

Journal: Chaos (Woodbury, N.Y.) 31:123134 http://dx.doi.org/10.1063/5.0067046

BibTeX Citation:

@article{hossain2021bifurcations,

title={Bifurcations, chaos, and multistability in a nonautonomous predator-prey model with fear},

author={Hossain, Mainul and Pal, Saheb and Kumar Tiwari, Pankaj and Pal, Nikhil},

journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},

volume={31},

number={12},

pages={123134},

year={2021},

publisher={AIP Publishing LLC}

}

6.

Journal Cover

Lyapunov exponent diagram in terms of largest exponent values evaluated in the (k–r) parameter plane of the system with Holling type-I functional response.

Fear Induced Multistability in a Predator-Prey Model

Authors: N C Pati, Shilpa Garai, Mainul Hossain, G C Layek & Nikhil Pal

Journal: IJBC 31(10):2150150 http://dx.doi.org/10.1142/S0218127421501509

BibTeX Citation:

@article{pati2021fear,

title={Fear induced multistability in a predator-prey model},

author={Pati, NC and Garai, Shilpa and Hossain, Mainul and Layek, GC and Pal, Nikhil},

journal={International Journal of Bifurcation and Chaos},

volume={31},

number={10},

pages={2150150},

year={2021},

publisher={World Scientific}

}

5.

Bifurcation diagrams of the system (2.2) corresponding to the bifurcation parameters k (= k1 = k2), k1 (keeping k2 = 0), and k2 (keeping k1 = 0) for the populations x, y, and z. We observe that all three forms of fear are capable of eliminating chaotic oscillations and establishing stable coexistence through the period-halving route.

A “Double” fear effect in a tri-trophic food chain model

Authors: Harendra Verma, Kwadwo Antwi-Fordjour, Mainul Hossain, Nikhil Pal, Rana Parshad & Pankaj Mathur

Journal: European Physical Journal Plus 136(9) http://dx.doi.org/10.1140/epjp/s13360-021-01900-3

BibTeX Citation:

@article{verma2021double,

title={A “Double” fear effect in a tri-trophic food chain model},

author={Verma, Harendra and Antwi-Fordjour, Kwadwo and Hossain, Mainul and Pal, Nikhil and Parshad, Rana D and Mathur, Pankaj},

journal={The European Physical Journal Plus},

volume={136},

number={9},

pages={1--17},

year={2021},

publisher={Springer}

}

2020

4.

Bifurcation diagram of the system with respect to the delay parameter 𝜏 in the range from 5 to 100..

Cooperation delay induced chaos in an ecological system

Authors: Saheb Pal, Mainul Hossain, Pijush Panday, N C Pati, Nikhil Pal, Joydev Chattopadhyay

Journal: Chaos (Woodbury, N.Y.) 30(8):083124 http://dx.doi.org/10.1063/5.0012880

BibTeX Citation:

@article{pal2020cooperation,

title={Cooperation delay induced chaos in an ecological system},

author={Pal, Saheb and Hossain, Mainul and Panday, Pijush and Pati, NC and Pal, Nikhil and Chattopadhyay, Joydev},

journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},

volume={30},

number={8},

pages={083124},

year={2020},

publisher={AIP Publishing LLC}

}

3.

Bifurcation diagrams of three submodels corresponding to the bifurcation parameter K. Rows represent submodels as indicated on the left, and columns 1, 2, and 3 correspond to susceptible, infected, and predator populations, respectively (also indicated on the top). Here we observe that increased fear (K) is able to eliminate the chaotic oscillations and make them disease-free.

Impact of fear on an eco-epidemiological model

Authors: Saheb Pal, Mainul Hossain, Pijush Panday, N C Pati, Nikhil Pal, Joydev Chattopadhyay

Journal: Chaos Solitons & Fractals 134:109718 http://dx.doi.org/10.1016/j.chaos.2020.109718

BibTeX Citation:

@article{hossain2020impact,

title={Impact of fear on an eco-epidemiological model},

author={Hossain, Mainul and Pal, Nikhil and Samanta, Sudip},

journal={Chaos, Solitons \& Fractals},

volume={134},

pages={109718},

year={2020},

publisher={Elsevier}

}

2.

Existence of multiple interior equilibria, and bistability behavior between the planar equilibrium point and the interior equilibrium point.

Fear Induced Stabilization in an Intraguild Predation Model

Authors: Mainul Hossain, Nikhil Pal, Sudip Samanta & Joydev Chattopadhyay

Journal: IJBC 30(04) http://dx.doi.org/10.1142/S0218127420500534

BibTeX Citation:

@article{hossain2020fear,

title={Fear induced stabilization in an intraguild predation model},

author={Hossain, Mainul and Pal, Nikhil and Samanta, Sudip and Chattopadhyay, Joydev},

journal={International Journal of Bifurcation and Chaos},

volume={30},

number={04},

pages={2050053},

year={2020},

publisher={World Scientific}

}

2018

1.

bifurcation diagram of the system (1) with respect to the bifurcating parameter c. Here we plot the maximum and minimum values of oscillations in blue and red colors, respectively.

Chaos Control in a Two Prey and One Predator System with Predator Switching

Authors: Saheb Pal, Mainul Hossain, Sudip Samanta & Nikhil Pal

Journal: In book: Advanced Computational and Communication Paradigms (pp. 435-441) http://dx.doi.org/10.1007/978-981-10-8237-5_42

BibTeX Citation:

@incollection{pal2018chaos,

title={Chaos control in a two prey and one predator system with predator switching},

author={Pal, Saheb and Hossain, Mainul and Samanta, Sudip and Pal, Nikhil},

booktitle={Advanced Computational and Communication Paradigms},

pages={435--441},

year={2018},

publisher={Springer}

}

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