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In this paper, an attempt has been made to estimate the biophysical parameters in an improved version of Morris–Lecar (M–L) neuron model in a noisy environment. To observe the influence of noisy stimulation in estimation procedure, a Gaussian white noise has been added to the membrane voltage of the model system. Estimation of the parameters has been investigated by a proposed algorithm. The denoising technique (local projection method) has been applied to reduce the influence of noisy stimuli and the effectiveness of the method is reported. The proposed scheme performs well for an excitable neuron model and provides good estimates between the estimated parameters and the actual values in a reasonable way. This approach can be used for parameter estimation for other nonlinear dynamical systems. [ABSTRACT FROM AUTHOR]

Abstract: We present a new ecological model, which displays “edge of chaos” (EoC) in parameter space. This suggests that ecological systems are not chaotic, instead, their dynamics can be characterized as short-term recurrent chaos. The system’s dynamics is unpredictable and admits bursts of short-term predictability. We also provide results, which suggest that fully developed chaos will rarely be observed in natural systems. [Copyright &y& Elsevier]

In this paper, an attempt has been made to understand the dynamics of a prey–predator system with multiple time delays where the predator population is regarded as a generalist type. In this regard, we consider a modified Holling–Tanner prey–predator system where a constant time delay is incorporated in the logistic growth of the prey to represent a delayed density dependent feedback mechanism and the second time delay is considered to account for the length of the gestation period of the predator. Predator’s interference in prey–predator relationship provides better descriptions of predator’s feeding over a range of prey–predator abundances, so the predator’s functional response is considered to be Type II ratio-dependent and foraging efficiency of predator largely varies with the refuge strategy of prey population. In accordance with previous studies, it is observed that delay destabilizes the system, in general and stability loss occurs via Hopf-bifurcation. In particular, we show that there exists critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Hopf bifurcation occurs when the delay parameters cross their critical values. Also, environmental stochasticity in the form of Gaussian white-noise plays a significant role to describe the system and its values. Numerical computation is also performed to validate and visualize different theoretical results presented. The analysis and results in this work are interesting both in mathematical and biological point of views. [ABSTRACT FROM AUTHOR]

Recent demographic experiments have demonstrated that both birth and survival in free-living animals are essentially affected due to having sufficient exposure to predators and further leaving physiological stress effects. In this paper, we have proposed and analyzed a predator–prey interaction model with Beddington–DeAngelis functional response (BDFR) and incorporating the cost of fear into prey reproduction. Stability analysis and the existence of transcritical bifurcation are studied. For the spatial system, the Hopf-bifurcation around the interior equilibrium, stability of homogeneous steady state, direction and stability of spatially homogeneous periodic orbits have been established. Using Normal form of the steady state bifurcation, the possibility of pitchfork bifurcation has been established. The impact of the level of fear and mutual interference on the stability and Turing patterns of the spatiotemporal system have been discussed in detail. Simulation results ensure that the fear of predator stabilizes the system dynamics and cost the overall population size of the species. [ABSTRACT FROM AUTHOR]