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We revisit the problem of random search walks in the two-dimensional (2D) space between concentric absorbing annuli, in which a searcher performs random steps until finding either the inner or the outer ring. By considering step lengths drawn from a power-law distribution, we obtain the exact analytical result for the search efficiency η in the ballistic limit, as well as an approximate expression for η in the regime of searches starting far away from both rings, and the scaling behavior of η for very small initial distances to the inner ring. Our numerical results show good overall agreement with the theoretical findings. We also analyze numerically the absorbing probabilities related to the encounter of the inner and outer rings and the associated Shannon entropy. The power-law exponent marking the crossing of such probabilities (equiprobability) and the maximum entropy condition grows logarithmically with the starting distance. Random search walks inside absorbing annuli are relevant, since they represent a mean-field approach to conventional random searches in 2D, which is still an open problem with important applications in various fields.

Animal behaviour is often quantified through subjective, incomplete variables that mask essential dynamics. Here, we develop a maximally predictive behavioural-state space from multivariate measurements, in which the full instantaneous state is smoothly unfolded as a combination of short-time posture sequences. In the off-food behaviour of the roundworm Caenorhabditis elegans, we discover a low-dimensional state space dominated by three sets of cyclic trajectories corresponding to the worm’s basic stereotyped motifs: forward, backward and turning locomotion. We find similar results in the on-food behaviour of foraging worms and npr-1 mutants. In contrast to this broad stereotypy, we find variability in the presence of locally unstable dynamics with signatures of deterministic chaos: a collection of unstable periodic orbits together with a positive maximal Lyapunov exponent. The full Lyapunov spectrum is symmetric with positive, chaotic exponents driving variability balanced by negative, dissipative exponents driving stereotypy. The symmetry is indicative of damped–driven Hamiltonian dynamics underlying the worm’s movement control.Animal behaviour is characterized by repeated movements which can be difficult to analyse quantitatively. Here, the authors apply a data-driven framework based on theory of dynamical systems to characterize nematode behaviour and explain its complexity through deterministic chaotic dynamics.

In this study, we analyze a generalist predator–prey model that includes a strong Allee effect in the prey population. We investigate the positivity and boundedness of solutions, identify ecologically relevant equilibrium points, and determine their stability conditions. Further, we analyze the transcritical, saddle-node, Hopf, Bogdanov-Takens, generalized-Hopf, and cusp bifurcations. Our numerical investigation shows that the model exhibits multiple stable states under similar parametric conditions, driven by bifurcation scenarios linked to the Allee effect. It also underscores the significant role of additional foods for predators in shaping system dynamics, unveiling scenarios ranging from the extinction of predators to their persistence, and the coexistence of both the species. Furthermore, our study delves into the impact of environmental white noise on predator–prey dynamics, introducing stochastic elements. We explore noise-induced transitions between two stable states within the system. Overall, our study highlights the complex dynamics of predator–prey interactions, emphasizing the role of Allee effect and additional food sources.

In ecological systems, the fear of predation risk may assert privilege to the prey species by restricting their exposure to potential predators, and also impose costs by constraining the exploration of optimal resources. In this paper, an eco-epidemic model of the predator–prey system is investigated by considering disease in prey population and selective behavior of predator; the cost of fear is taken as affecting the reproduction and intraspecies competition of vulnerable prey population, and also lowers the disease transmission; the predators are assumed to cooperate with each other for the hunting while the susceptible/infected prey population takes refuge. Numerical observations of the system demonstrate that the cost of fear causing a reduction in the birth rate of susceptible prey has a destabilizing role, whereas the levels of fear responsible for the increase in the intraspecies competition of susceptible prey and eradication of the disease prevalence have the capacity to stabilize an otherwise unstable system. The intensity of disease prevalence potentially affects the dynamics of the ecosystem by altering its stability around the infection-free state and the coexistence of prey and predator species. However, refuge taken by the susceptible/infected prey has the potential to restore the stability of the system. Moreover, the chaotic nature of the system is observed if the preference of predators for susceptible prey or hunting cooperation of predators exceeds a fixed value. We also investigate the dynamics of the system by letting some of the model parameters to vary with time. Our numerical results for the seasonally forced system showcase different dynamical features including periodic solutions, higher periodic solutions, bursting patterns, and chaos.

Motif discovery is a powerful and insightful method to quantify network structures and explore their function. As a case study, we present a comprehensive analysis of regulatory motifs in the connectome of the model organism Caenorhabditis elegans ( C. elegans ). Leveraging the Efficient Subgraph Counting Algorithmic PackagE (ESCAPE) algorithm, we identify network motifs in the multi-layer nervous system of C. elegans and link them to functional circuits. We further investigate motif enrichment within signal pathways and benchmark our findings with random networks of similar size and link density. Our findings provide valuable insights into the organization of the nerve net of this well-documented organism and can be easily transferred to other species and disciplines alike. Graphical abstract

In this paper, we consider a two-species predator–prey model with fading memory, where the growth rate of prey species is subject to predation induced fear. Growth rate of predator species depends not only on the present density of prey but also on the past densities with diminishing impact. As the societal activities and behavioral practices influence carrying capacity of any species, we consider the density dependent carrying capacity of prey species instead of a constant. As fear on growth rate and societal activities on carrying capacity entail some time lags to show their effect, so we incorporate two delay parameters to corroborate this in the modeling phenomenon. Feasibility criteria of equilibria and their stability analysis are carried out. We observe that fear parameter and predation rate have destabilizing effect on the system’s dynamics, whereas parameter representing intensity of fading memory has stabilizing impact. We also distinguish stability and instability regions in different parametric planes. With increasing value of production factor from negative to positive, stability region decreases. The system also shows multiple stability switching phenomenon with respect to delay parameters. Solutions show chaotic behavior for a range of fear response delay both in the absence and presence of other delay parameter.

The foraging behavior of animals is a paradigm of target search in nature. Understanding which foraging strategies are optimal and how animals learn them are central challenges in modeling animal foraging. While the question of optimality has wide-ranging implications across fields such as economy, physics, and ecology, the question of learnability is a topic of ongoing debate in evolutionary biology. Recognizing the interconnected nature of these challenges, this work addresses them simultaneously by exploring optimal foraging strategies through a reinforcement learning (RL) framework. To this end, we model foragers as learning agents. We first prove theoretically that maximizing rewards in our RL model is equivalent to optimizing foraging efficiency. We then show with numerical experiments that, in the paradigmatic model of non-destructive search, our agents learn foraging strategies which outperform the efficiency of some of the best known strategies such as Lévy walks. These findings highlight the potential of RL as a versatile framework not only for optimizing search strategies but also to model the learning process, thus shedding light on the role of learning in natural optimization processes.

Fear of predators as an indirect effect of predation is a well-observed phenomenon in natural predator–prey communities. After being popularized by Wang et al. in 2016 (J. Math. Biol., 73:1179–1204), the indirect effect of fear has been studied through its incorporation into several mathematical models in different ecological settings. The impact of fear effect in a three-species food chain model, where the top predator is a generalist predator, is not yet investigated. In the present work, a three-species food chain model incorporating the fear of predators is investigated, where the fear of generalist predator impedes the growth rate of the specialist predator, and the fear of specialist predator reduces the birth rate of the prey. We derive criteria for the existence of all possible non-negative equilibrium points and provide some remarks on their local stability. Additionally, the conditions for the occurrence of various local bifurcations have been established. In the absence of fear, we show that the model exhibits chaotic dynamics via periodic-doubling route when the birth rate of the prey is varied. Furthermore, we observe that fear can alter the stability of the model from a chaotic zone to a stable zone via period-halving route. It is also observed that with an appropriate choice of parameter values, fear can act as a damping mechanism, preventing the unwanted blow-up of the generalist predator in finite time. We provide numerical simulations to support our analytical findings.

Optimization is an important and fundamental challenge to solve optimization problems in different scientific disciplines. In this paper, a new stochastic nature-inspired optimization algorithm called Pelican Optimization Algorithm (POA) is introduced. The main idea in designing the proposed POA is simulation of the natural behavior of pelicans during hunting. In POA, search agents are pelicans that search for food sources. The mathematical model of the POA is presented for use in solving optimization issues. The performance of POA is evaluated on twenty-three objective functions of different unimodal and multimodal types. The optimization results of unimodal functions show the high exploitation ability of POA to approach the optimal solution while the optimization results of multimodal functions indicate the high ability of POA exploration to find the main optimal area of the search space. Moreover, four engineering design issues are employed for estimating the efficacy of the POA in optimizing real-world applications. The findings of POA are compared with eight well-known metaheuristic algorithms to assess its competence in optimization. The simulation results and their analysis show that POA has a better and more competitive performance via striking a proportional balance between exploration and exploitation compared to eight competitor algorithms in providing optimal solutions for optimization problems.