University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Applied Mathematics

The most important fact in the field of theoretical ecology and evolutionary biology is the strategy of predation for predators and avoidance of prey from predator attack. A lot of experimental works suggest that the reduction of prey depends on both direct predation and fear of predation. We explore the impact of fear effect and mutual interference among predators into a three-species food chain model. In this manuscript, we have considered a tri-topic food chain model with Beddington–DeAngelis functional response between interacting species, incorporating the reduction of prey and intermediate predator growth due to the fear of intermediate and top predator, respectively. We have provided parametric conditions for existence of biologically feasible equilibria as well as their local and global stability. We have established conditions of transcritical, saddle-node and Hopf bifurcation about different equilibria. Finally, we have performed some numerical investigations to justify analytical findings. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.

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Nonlinear Dynamics

Chaotic dynamics of a tri-topic food chain model with Beddington–DeAngelis functional response in presence of fear effect

A new compact stars nonsingular model is presented with the generalized Bardeen-Hayward mass function. Generalized Bardeen-Hayward described the regular black hole, however, due to its regularity or nonsingular nature we were inspired to construct an anisotropic compact stars model. Along with the ansatz mass function, we coupled it with a linear equation of state (EoS) to find the solutions of field equations. Indeed, the new solutions are physically viable in all physical ground. The energy conditions and Tolman-Oppenheimer-Volkoff (TOV)-equation are well satisfied signifying that the mass distribution is physically possible and at equilibrium. Also, the static stability criterion, the causality condition and Abreu's stability condition hold good and therefore configurations are physically static stable. The same condition is further supported by the condition that the adiabatic index, which is greater than the Newtonian limit, i.e. τr(r) > 4/3. It is also noticed that the bag constant Bg is proportional to the surface density in our model. © 2021 World Scientific Publishing Company.

Modern Physics Letters A

Anisotropic compact stars model with generalized Bardeen-Hayward mass function

arXiv preprint arXiv:2107.

Arbitrary Measurement dependence in tripartite non-locality

In this paper, we have considered stochastic insect outbreak model in presence of Michaelis-Menten type of harvesting. The growth of the insect species is taken as delayed logistic type together with a multiplicative noise term. The impact of internal environmental disturbances on the insect population is taken into account by adding an additive noise term in the model. The effects of the noises, cross correlation strength of the noises and time delay on the insect population are investigated and observed very rich dynamical behaviors. It is ascertained that multiplicative noise reduces population size greatly than additive noise. As usual, increase of harvesting of insect species reduces the population size at faster rate. Regime shift is possible depending on multiplicative noise only in contrast it is not possible via only additive noise. One of the key finding is the noise-delayed switching phenomenon for negatively correlated noises. © 2021 IOP Publishing Ltd.

Physica Scripta

Delay induced dynamical behaviors in a stochastic insect outbreak model in presence of Michaelis-Menten type harvesting

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point (DFE) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov-Takens bifurcation (BT) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment. © The authors. Published by EDP Sciences, 2021.

Mathematical Modelling of Natural Phenomena

Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

The transport properties of the weakly nonlinear (WNL) two-dimensional (2D) quasilongitudinal dust lattice mode is studied in an experimentally realized highly viscous, strongly coupled, weakly ionized plasma [V. E. Fortov, Phys. Rev. Lett. 109, 055002 (2012)10.1103/PhysRevLett.109.055002]. The WNL dynamics is found to be described by a 2D dissipative-dispersive nonlinear partial differential equation. The analytical and computational (for gas discharge plasma parameters) results predict strong viscosity induced Shilnikov homoclinic chaos, which, in turn, can cause a phase transition. © 2021 American Physical Society.

Physical Review E

Homoclinic chaos in strongly dissipative strongly coupled complex dusty plasmas

Non-linear dynamical behaviour of electron acoustic waves (EAWs) is studied in a magnetized non-thermal plasma (containing inertial cold electrons, inertialess hot electrons following non-thermal distribution function, and static ions) via a fluid dynamical approach. A linear dispersion relation is derived and the propagation of two possible modes and their evolution are studied through the different plasma configuration parameters, such as non-thermality and external magnetic field strength. In a non-linear perturbation regime, a reductive perturbation technique is employed to derive the non-linear evolution equation and the analysis is executed for travelling plane waves in terms of a non-linear dynamical system to enlighten the numerous aspects of the phase space dynamics. The results of numerical simulation predict the existence of a wide class of non-linear structures, namely solitonic, periodic, quasiperiodic, and chaotic depending upon different controlling plasma parameters. Also, Poincaré return map analysis confirms these non-linear structures of the EAWs. © 2021 Wiley-VCH GmbH

Contributions to Plasma Physics

Non-linear behaviour of electron acoustic wave dynamics in a magnetized plasma with non-thermal hot electrons

In this article, we have studied a memory dependent prey–predator model with logistic type prey growth subject to the Allee effect and Holling type-III functional response. To include the memory effect, we have used here a fractional order system. The model contains at most four equilibrium points among which one is trivial, two are axial, and the last one is interior. Here we have studied behavior of these four equilibrium points using eigen analysis method. Our investigation shows that the trivial equilibrium point is stable for strong Allee effect, and unstable for weak Allee effect. Between the two axial equilibrium points, one is stable under certain condition but the other is always unstable. This unstable equilibrium point exists only for strong Allee case. The interior equilibrium point arises when the axial equilibrium point is unstable. Stability condition of this interior equilibrium point depends on the parametric relationship. The schematic diagram divides the a-p plane into five sub-regions in both the cases of memory dependent and memory less system. The number and nature of the equilibrium points in different sub-regions are different. Finally, we have drawn the bifurcation diagrams considering all the equilibrium points in different sub-regions and the results are concluded at the end. © 2020 John Wiley &amp; Sons Ltd

Computational and Mathematical Methods

Unraveling the combined actions of a Holling type III predator–prey model incorporating Allee response and memory effects

In any business memory effect has great importance in inventory management as memory or past history cannot be ignored from the practical life of the inventory system. Many exogenous inventory parameters and factors at a given time depends not only their current values but also on the past histories. Thus an inventory management is a non Markovian process which can be tackled with memory dependent kernel of fractional derivatives. Another important factor of inventory management is deterioration of items which is directly related with memory effect as long memory of high rate of deterioration leads to poor impact on the business. Effect of long memory on deterioration of items have been studied in this paper using memory kernel of fractional derivatives. Fractional integration has been used to derive fractional order holding cost, deterioration cost, shortage cost and opportunity cost. Our analysis shows that for gradually increasing memory effect profit gradually increases. Our model is developed as a memory dependent inventory model. ©2021 L&amp;H Scientific Publishing, LLC. All rights reserved.

Journal of Applied Nonlinear Dynamics

Study of Memory Effect in an Inventory Model with Constant Deterioration Rate

The paper investigates the crossing sea state situation characterized by two obliquely interacting water wave systems having different carrier frequencies in finite depth domain. Nonlinear evolution equations are derived to study the instability properties of two obliquely interacting uniform wave trains for both unidirectional and bidirectional perturbations. It is found that the growth rate of modulational instability increases with the decrease in angle of interaction of the two wave systems and also with the increase in the ratio of the carrier wave numbers of the two wave systems. The growth rate of instability decreases with the increase in water depth, while it increases with the increase in wave steepness of the second wave system. © 2021 Author(s).