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In this paper, a prey-predator model in polluted environment with disease in prey has been proposed and studied. It is assumed that only prey population is prone to disease whereas, both the populations are affected by the pollutant. Boundedness of the solution of the system is discussed. Existence of all possible equilibrium points has been established. Using Routh Hurwitz criterion, local stability of all the possible equilibrium points has been obtained. Also, interior equilibrium point has been proved to be globally asymptotically stable using Lyapunov function. Then time delay has been introduced in the system making the model more realistic. Existence and direction of Hopf bifurcation in the delay model has been established using normal form theory and center manifold theorem. By taking a set of hypothetical and biologically feasible parameters, model has been studied numerically using MATLAB and the effect of pollutant on the system has been deduced. © 2021 the author(s).

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Department of Mathematics

Fulltext

Communications in Mathematical Biology and Neuroscience

Dynamical analysis of polluted prey-predator system with infected prey

We study the multi-boundary entanglement structure of the states prepared in (1+1) and (2+1) dimensional Chern-Simons theory with finite discrete gauge group G. The states in (1+1)-d are associated with Riemann surfaces of genus g with multiple S1 boundaries and we use replica trick to compute the entanglement entropy for such states. In (2+1)-d, we focus on the states associated with torus link complements which live in the tensor product of Hilbert spaces associated with multiple T2. We present a quantitative analysis of the entanglement structure for both abelian and non-abelian groups. For all the states considered in this work, we find that the entanglement entropy for direct product of groups is the sum of entropy for individual groups, i.e. EE(G1× G2) = EE(G1) + EE(G2). Moreover, the reduced density matrix obtained by tracing out a subset of the total Hilbert space has a positive semidefinite partial transpose on any bi-partition of the remaining Hilbert space. © 2020, The Author(s).

Journal of High Energy Physics

Multi-boundary entanglement in Chern-Simons theory with finite gauge groups

In this paper, we discuss the dynamics of alterations and rearrangements of a non-autonomous dynamical system generated by the family F. We prove that while insertion/deletion of a map in the family F can disturb the dynamics of a system, the dynamics of the system does not change if the map inserted/deleted is feeble open. In the process, we prove that if the inserted/deleted map is feeble open, the altered system exhibits any form of mixing/sensitivity if and only if the original system exhibits the same. We extend our investigations to properties like equicontinuity, minimality, and proximality for the two systems. We prove that any finite rearrangement of a non-autonomous dynamical system preserves the dynamics of original system if the family F is feeble open. We also give examples to show that the dynamical behavior of a system need be not be preserved under infinite rearrangement. © 2019, Iranian Mathematical Society.

Bulletin of the Iranian Mathematical Society

Alterations and Rearrangements of a Non-autonomous Dynamical System

Let X ⊂ AZd be a 2-dimensional subshift of finite type. We prove that any 2-dimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general d-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space X to exhibit periodic points. © AGT, UPV, 2019.

Applied General Topology

Matrix characterization of multidimensional subshifts of finite type

We study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self-maps on a compact space X. We derive necessary and suﬃcient conditions for the system to exhibit complex dynamical behavior. In the process we discuss properties like transitivity, weakly mixing, topologically mixing, minimality, sensitivity, topological entropy, and Li-Yorke chaoticity for the non-autonomous system. We also give examples to prove that the dynamical behavior of the nonautonomous system in general cannot be characterized in terms of the dynamical behavior of its generating functions. © 2017 Topology Proceedings.

Topology Proceedings

Dynamics of non-autonomous discrete dynamical systems

In this paper, we investigate the dynamics of a non-autonomous dynamical system (X,F) generated by a uniformly convergent sequence of continuous self maps on X. We relate the dynamical behavior of (X,F) with the dynamical behavior of the limiting system (and vice versa). In the process, we relate properties like equicontinuity, minimality, various forms of mixing and sensitivities, dense periodicity and denseness of proximal pairs (cells) for the two systems. We also give examples to investigate the necessity of the conditions imposed. © 2018 Elsevier B.V.

Topology and its Applications

On dynamics generated by a uniformly convergent sequence of maps

In this paper, we study the dynamics induced by finite commutative relation. We prove that the dynamics generated by such a non-trivial collection cannot be transitive/super-transitive and hence cannot exhibit higher degrees of mixing. As a consequence we establish that the dynamics induced by such a collection on the hyperspace endowed with any admissible hit and miss topology cannot be transitive and hence cannot exhibit any form of mixing. We also prove that if the system is generated by such a commutative collection, under suitable conditions the induced system cannot have dense set of periodic points. In the end we give example to show that the induced dynamics in this case may or may not be sensitive. © AGT, UPV, 2016.

Induced dynamics on the hyperspaces

We discuss conditions under which an affine automorphism of a compact nilmanifold is almost automorphic, and the structure of such automorphisms from dynamical as well as algebraic points of view. © 2014 Cambridge University Press.

Ergodic Theory and Dynamical Systems

Affine almost automorphic actions on compact nilmanifolds

Most of the real world scenes have a very high dynamic range (HDR). The mobile phone cameras and the digital cameras available in market are limited in their capability in both the range and spatial resolutions. Same argument can be posed about the limited dynamic range of display devices which further differ in spatial resolution and aspect ratio. In this paper, we address the problem of displaying the high contrast low dynamic range (LDR) image of a HDR scene in a display device which has different spatial resolution compared to that of the capturing device. We want to achieve this task while preserving the salient scene contents. The solution proposed in this work can be employed with any camera which has the ability to shoot multiple differently exposed images of a scene. Further, the proposed solutions provide the flexibility in the depiction of entire contrast of the HDR scene as an LDR image with user specified spatial resolution. This task is achieved through an optimized content aware retargeting framework which preserves the salient features apart from a novel algorithm to fuse multi-exposure images. We show that the proposed approach performs exceedingly well in the generation of high contrast LDR image of varying spatial resolutions. © 2014 IEEE.

Proceedings of the 5th International Conference on Confluence 2014: The Next Generation Information Technology Summit

Efficient image retargeting for high dynamic range scenes

Dynamical systems are systems that evolve with time. In this paper, we study the dynamics displayed by the combined effect of the join of distinct dynamical systems. The relation, obtained thus, is a set-valued function. We compare the various dynamical properties of such a relation with its individual defining components, as well as its induced counterpart on the hyperspace. Some comparisons can be easily derived, but this study also leads to various questions that have been proposed in this article. © 2010 Topology Proceedings.

Combined dynamics on hyperspaces

Let (X,d) be a compact metric space and (K(X),dH) be the space of all non-empty compact subsets of X equipped with the Hausdorff metric dH. The dynamical system (X,f) induces another dynamical system (K(X),f{topbar}). We study the relations between the various forms of sensitivity of the systems (X,f) and (K(X),f{topbar}). We prove that all forms of sensitivity of (K(X),f{topbar}) partly imply the same for (X,f), and the converse holds in some cases. © 2010 Elsevier B.V.

Inducing sensitivity on hyperspaces

In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the known results come up as corollaries to our results. We also discuss some metric related dynamical properties on the hyperspace that cannot be deduced for the base dynamics. © Universidad Politécnica de Valencia.