Abstract
In the current manuscript, an attempt has been made to understand the dynamics of a time-delayed predator-prey system with modified Leslie-Gower and Beddington-DeAngelis type functional responses for large initial data. In Ref. Upadhyay and Agrawal, 83(2016) 821–837, it was shown that the model possesses globally bounded solutions, for small initial conditions, under certain parametric restrictions. Here, we show that actually solutions to this model system can blow-up in finite time, for large initial condition, even under the parametric restrictions derived in Ref. Upadhyay and Agrawal, 83(2016) 821–837. We prove blow-up in the delayed model, as well as the non-delayed model, providing sufficient conditions on the largeness of data, required for finite time blow-up. Numerical simulations show that actually the initial data does not have to be very large, to induce blow-up. The spatially explicit system is seen to possess non-Turing instability. We have also studied Hopf-bifurcation direction in the spatial system, as well as stability of the spatial Hopf-bifurcation using the central manifold theorem and normal form theory.
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Articles in the same Issue
- Frontmatter
- The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation
- Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn–Hilliard Equation
- On the Mittag–Leffler Stability of Impulsive Fractional Solow-Type Models
- Non-similarity Solutions for Viscous Dissipation and Soret Effects in Micropolar Fluid over a Truncated Cone with Convective Boundary Condition: Spectral Quasilinearization Approach
- Numerical Simulation of the Supersonic Disk-Gap-Band Parachute by Using Implicit Coupling Method
- Stochastic-Based RANS-LES Simulations of Swirling Turbulent Jet Flows
- Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections
- Hermite Pseudospectral Method for the Time Fractional Diffusion Equation with Variable Coefficients
- Multiple-Wave Solutions to Generalized Bilinear Equations in Terms of Hyperbolic and Trigonometric Solutions
- Experimental and Simulation Analysis of the Successful Production of Heavy-Gauge Steel Plate by the Clad Rolling Process
- Jacobi Collocation Approximation for Solving Multi-dimensional Volterra Integral Equations
- A Note on Hidden Transient Chaos in the Lorenz System
- Finite Time Blow-up in a Delayed Diffusive Population Model with Competitive Interference
Articles in the same Issue
- Frontmatter
- The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation
- Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn–Hilliard Equation
- On the Mittag–Leffler Stability of Impulsive Fractional Solow-Type Models
- Non-similarity Solutions for Viscous Dissipation and Soret Effects in Micropolar Fluid over a Truncated Cone with Convective Boundary Condition: Spectral Quasilinearization Approach
- Numerical Simulation of the Supersonic Disk-Gap-Band Parachute by Using Implicit Coupling Method
- Stochastic-Based RANS-LES Simulations of Swirling Turbulent Jet Flows
- Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections
- Hermite Pseudospectral Method for the Time Fractional Diffusion Equation with Variable Coefficients
- Multiple-Wave Solutions to Generalized Bilinear Equations in Terms of Hyperbolic and Trigonometric Solutions
- Experimental and Simulation Analysis of the Successful Production of Heavy-Gauge Steel Plate by the Clad Rolling Process
- Jacobi Collocation Approximation for Solving Multi-dimensional Volterra Integral Equations
- A Note on Hidden Transient Chaos in the Lorenz System
- Finite Time Blow-up in a Delayed Diffusive Population Model with Competitive Interference