A gauss type prey - predator model is considered with Allee effect and Holling II response. Fractional order two species system discretized. The discretized exhibits much richer complex dynamics than its corresponding continuous version.Bifurcation types like flip, neimark sacker chaos exist in the system.Existence of positive fixed points established local stability discrete fractional discussed variational matrix. It also shown that allows a flip bifurcation bifurcation. Rich dynamical...

In this work, we establish oscillation theorems for damped fractional order difference equation of the form Δ[δ(k)Δγy(k)]+ρ(k)Δγy(k)+ξ(k)Z[Y(k)]=0,k≥k0>0 where Y(k)=∑u=k0k−1+γ(k−u−1)−γy(u) and Δγ defined as operator Riemann-Liouville derivative γ ∈ (0, 1]. By using Riccati type transformation techniques, arrive at some new sufficient conditions all solutions equation.

This study presents numerical examples of Discrete Fractional Order Prey Predator interactions with Functional Response. The process discretization is applied and the version discrete equations obtained. Fixed points are determined stability around fixed analyzed. Also theoretical analysis has been verified from simulations, which help better understanding proposed system. Rich dynamics system exhibited by Bifurcation diagram Periodic Oscillations for suitable parameters values. Â

Herein, we examine the oscillatory behavior of all solutions a fractional order difference equations with damping term formwhere G(t) = t-1+α s=t 0 (ts -1) -α u(s) and ∆ α denotes Riemann-Liouville operator < ≤ 1.We arrive at some new sufficient conditions for oscillation damped using generalized riccati type transformation technique under suitable conditions.

The aim of this paper is to analyze the chaotic dynamics a novel 2D fractional order discrete Ushiki map using Caputo-like delta difference operator. dynamical nature proposed examined with evolution time states and bifurcation diagrams. In addition, control law aimed at stabilizing synchronization are also presented. Numerical examples exhibited demonstrate validity theoretical findings study.

In this work titled Stability, Bifurcation, Chaos: Discrete prey predator model with step size, by Forward Euler Scheme method the discrete form is obtained. Equilibrium states are calculated and stability of equilibrium dynamical nature examined in closed first quadrant R2  help variation matrix. It observed that system sensitive to initial conditions also parameter values. The investigated assistance Lyapunov Exponent, bifurcation diagrams, phase portraits chaotic behavior identified....

The main objective of this work is to obtain some new sufficient conditions that are essential for the oscillation solutions forced nonlinear discrete fractional equations form \begin{align*}\Delta\left[\Delta^\mu(u(j))\right]+\eta(j)\Phi(u(j))=\psi(j), \ j\in N_0\end{align*}where \(\Delta^{\mu-1}u(0)=u_0\); \(\Delta u(j)=u(j+1)-u(j)\) and \(\Delta^\mu\) defined as difference operator Riemann-Liouville (R-L) derivative order \(\mu\in(0,1]\) \(N_0=\{0,1,2,\cdots\}\). Numerical examples...

Wireless sensor networks (WSNs) are at risk to cyber attacks and thus security is of vital concern. WSN a soft target for worm due fragile defence mechanism in the network . A single unsecured node can essentially propogate complete via communication. Mathematical epidemic models useful study propagation worms WSNs. This work considers fractional order discrete model attacking spreading dynamics WSNs form The proposed probed with assistance stability theory. Basic reproduction number (R0)is...

The refuge of prey species is a biological factor necessary for the coexistence and hence it yet another great interest due to defensive properties against predation. We propose class discrete differential algebraic predator system with Holling Type II functional response refuge. found possess trivial, semi-trivial interior equilibrium states existing under certain conditions. Also we examine existence uniqueness solutions system. Dynamical behaviour investigated through linear stability...

This paper aims to examine the dynamics of a variation nonlinear SIR epidemic model. We analyze complex dynamic nature discrete-time model by discretizing continuous subject treatment and immigration effects with Euler method. First all, we show existence equilibrium points in reducing three-dimensional system two-dimensional system. Next, stability conditions obtained positive point visibility flip bifurcation. A feedback control strategy is applied chaos occurring after certain period...

In this study, the dynamics of a discrete-time plant-herbivore model obtained using forward Euler method are discussed. The existence fixed points is investigated. A topological classification made to examine behavior positive point where plant and herbivore coexist. addition, conditions direction Neimark-Sacker bifurcation investigated theory. Hybrid control applied chaos caused by bifurcation. Examples including time series figures, phase portraits maximum Lyapunov exponent provided...

Mathematical models are useful in examining the effect of an infection on populations. Conditions involving spread and control disease calculated by analyzing mathematical models, so that it is possible to have information about behavior infection. This article includes dynamic a discrete-time SIS epidemic model with treatment. Existence conditions fixed points obtained, stability analysis performed for these points. The bifurcation obtained endemic point investigated. Depending coefficient,...

Abstract In this present work, a class of Fractional Order Predator-Prey System (FOPP) in discrete time with Holling type II functional response incorporating prey refuge the form <?CDATA \begin{eqnarray*}x(i+1)=x(i)+\frac{{h}^{v}}{\Gamma (1+v)}\left[rx(i)-r{x}^{2}(i)-a\left(\frac{(1-\mu )x(i)}{(1-\mu )x(i)+b}\right)y(i)\right]\\ y(i+1)=y(i)+\frac{{h}^{v}}{\Gamma (1+v)}\left[-cy(i)+d\left(\frac{(1-\mu )x(i)+b}\right)y(i)\right]\end{eqnarray*}?> <mml:math...

Abstract Stability and bifurcation analysis for a two spices discrete fractional order system by introducing square root response function of the form <?CDATA \begin{eqnarray*}\begin{array}{l}x(j+1)=x(j)+ \displaystyle\frac{{h}^{\alpha }}{\Gamma (1+\alpha )}[\mu x(j)-\mu {x}^{2}(j)-\sigma \sqrt{x(j)y(j)}]\\ y(j+1)=y(j)+ )}[\eta \sqrt{x(j)y(j)}-\beta y(j)]\end{array}\end{eqnarray*}?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mtable columnalign="left">...

This paper aims to establish some new sufficiency conditions for the oscillatory behavior of solutions a forced non linear difference equation fractional order with damping term Δ(Δμu(l))+γ(l)Δμu(l)+ρ(l)Ψ(u(l))=ϕ(l),l∈ℕ0Δ(μ−1)u(0)=u(0)=u0 assistance properties Riemann-Liouville (RL) sum and operators. Suitable examples are provided demonstrate applicability derived outcomes.

Abstract In this present work, new oscillation theorems for discrete forced nonlinear equations with fractional order of the form <?CDATA \begin{eqnarray*}\Delta [\gamma (\ell )\phi (u(\ell )){\Delta }^{\mu }(u(\ell ))]+q(\ell )F[G(\ell )]=\eta ),\ell \ge {\ell }_{0}\gt 0\end{eqnarray*}?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mo stretchy="false">[</mml:mo> <mml:mi>γ</mml:mi>...