Vol. 10, No. 1 (2021): Regular Issue

This paper investigates a predator-prey system with Allee effect and Holling type-II functional response consisting of phytoplankton as prey and zooplankton as a predator. For the non-spatial system, we analyzed the stability, the existence of Hopf bifurcation at the coexistence equilibrium and stability of bifurcating periodic solutions are obtained. Moreover, the diffusion driven instability, Hopf bifurcation of the corresponding spatial system with zero flux boundary conditions and Turing instability region regarding parameters are established. Numerical simulations are provided to illustrate theoretical results.

In this paper, the dynamics of an HIV infection model with absorption and saturation incidence are proposed and analyzed. Further, we introduce a time delay to the model, which describes a time between infected cells and excretion of the viral particles. This model is used to explain existence, characteristic equations, and stability of infected and disease free steady states. Numerical simulations are provided to illustrate the theoretical results.

In this paper, we prove the uniqueness of weak solutions $(f, Q)$ to the phase-lock equations with $f_0 \in L^2$ and $Q_0 \in L^3$ when the space dimension $d = 3.$ We also prove the uniqueness of weak solutions $(f, a)$ to the Ginzburg-Landau equations with $(f_0, a_0) \in L^p \times L^p$ and $1 < p < 2$ when $d = 1.$ We will also present a result on the decay of $Q$ as time $t\to\infty.$

In this paper we consider the quadratic stochastic operators describing evolution of a bisexual population. We establish correlation between such operators and evolutionary games, namely demonstrate that Volterra quadratic stochastic operator with degenerate payoff matrix is non-ergodic and corresponding evolutionary game is rock-paper-scissors game. To prove this statements we study the asymptotic behavior of trajectories of the Volterra quadratic stochastic operators with the non-hyperbolic fixed points.

In this paper we have studied the dynamical behaviors of stage-structured-prey and predator model with linear harvesting of both mature prey and predator. Optimal harvesting policy, positivity, boundedness and Hopf-bifurcation have been studied. Finally, some graphical and numerical simulations are given in order to validate our analytical and theoretical findings.

The hybrid systems are used to study many engineering problems over a period of time. Now, we are adding another parameter called delay to make the hybrid systems to model any biological problems in future. We are extending the system of hybrid fuzzy differential equation to hybrid fuzzy mixed delay differential equation in this research article. The Runge-Kutta method of order four has been used to solve the problem by converting the mixed delay differential equation to multiple retarded delay differential equation. Finally, the numerical example is presented and the results are analyzed.

Distributed delays modeled by `weak generic kernels' are introduced in two well-known coupled van der Pol systems, as well as a chaotic van der Pol-Rayleigh system with parametric forcing. The systems are closed via the `linear chain trick'. Linear stability analysis of the systems and conditions for Hopf bifurcation that initiates oscillations are investigated, including deriving the normal form at bifurcation, and deducing the stability of the resulting limit cycle attractor. The value of the delay parameter $a = a_{Hopf}$ at Hopf bifurcation picks out the onset of Amplitude Death(AD) in all three systems, with oscillations at larger values (corresponding to weaker delay). In both van der Pol systems, the Hopf-generated limit cycles for $a > a_{Hopf}$ turn out to be remarkably stable under very large variations of all other system parameters beyond the Hopf bifurcation point, and do not undergo further symmetry breaking, cyclic-fold, flip, transcritical or Neimark-Sacker bifurcations. Numerical simulations reveal strong distortion and rotation of the limit cycles in phase space as the parameters are pushed far into the post-Hopf regime, and also reveal other features, such as how the oscillation amplitudes and time periods of the physical variables on the limit cycle attractor change as the delay and other parameters are varied. For the chaotic system, very strong delays may still lead to the cessation of oscillations and the onset of AD. Varying of the other important system parameter, the parametric excitation, leads to a rich sequence of dynamical behaviors, with the bifurcations leading from one regime (or type of attractor) into the next being carefully tracked.

A cloud-based framework for security of electronic patient record, in telediagnosis of Parkinson's disease (PD) speech signal has been proposed in this paper. The security and authenticity of patient's personal information is achieved using proposed Discrete Cosine Transform-Singular Value Decomposition (DCT-SVD) based audio watermarking technique. The automatic classification of PD affected speech signal from healthy person's speech signal requires high computational accuracy and in this work, it is addressed by extracting various time frequency features for the Support Vector Machine (SVM) classifier. In the proposed framework the speech signal of PD suspected person is recorded by a mobile application. The personal information is securely embedded in this speech signal using proposed DCT-SVD based audio watermarking technique, before transmitting to cloud for automatic classification. To ensure the security of electronic patient record (EPR), proposed watermarking technique is tested against various signal processing attacks and the performance of classifier has been evaluated by computing classification sensitivity, specificity, accuracy and area under the curve of receiver operating characteristics (ROC). The theoretical proofs and experimental results, show that proposed framework provides telediagnosis of PD affect patients without compromising the security and privacy of patient's records. The classification accuracy of $89\%$ with high data payload of $6kbps$ is proposed leading to a smart and secure e-healthcare application.

We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which govern a relation between subsets of a metric space to build a porous self-similar structure. Examples are provided to confirm that the definition satisfies a large class of self-similar fractals. The new concepts create new frontiers for fractals and chaos investigations.

In the paper we prove a conjecture of U.A. Rozikov and R. Varro about globally attractiveness of a unique nonhyperbolic fixed point of the normalized gonosomal evolution operator of a sex linked inheritance.

In this paper we modify Holling-Tanner predator-prey model by using type-IV functional response in prey species in lieu of type-II functional response. Harvesting is used in predator as well as prey species. This model is compared with a special type of Kolmogorov model. In the case of quadratic harvesting, the fixed points are computed after nondimensionalization. For the non-existence of periodic orbits in the first quadrant we apply a condition of the general Kolmogorov model to exist a Dulac function. We show that this system does not have periodic orbits with the help of numerical simulation and graphical representation.

The paper concerns with Wilson-Cowan neural model. The main novelty of the study is that besides the traditional singularity of the model, we consider singular impulses. A new technique of analysis of the phenomenon is suggested. This allows to consider the existence of solutions of the model and bifurcation in ultimate neural behavior observed through numerical simulations. The bifurcations are reasoned by impulses and singularity in the model and they concern the structure of attractors, which consist of newly introduced sets in the phase space such that medusas and rings.