Giuseppe Palomba and the Lotka-Volterra equations

Gandolfo, Giancarlo

doi:10.1007/s12210-008-0023-7

Cited by 48 publications

(15 citation statements)

References 7 publications

(9 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many researches using different concepts of differentiations have been done and some good predictions were obtained. [1][2][3][4][5][6][7][8][9][10][11][12] However, the real observation is more complex than the suggested model. For instance, it has been observed by many field worker biologists, and also many videos played by national geography channel show a group of hyena killing and eating lions.…”

Section: Introductionmentioning

confidence: 99%

A new nonlinear triadic model of predator–prey based on derivative with non-local and non-singular kernel

Alkahtani

Atangana

Koca

2016

Advances in Mechanical Engineering

View full text Add to dashboard Cite

The model of predator-prey has been used by many researchers to predict the animal growth population in many countries in the world. However, the system of equations used in these models assumes a density of prey and predator, respectively, but when looking at the real-world situation, most of the time we have some prey that act at the same time like a predator, for instance, hyena, and also some predators that act as a prey, for instance, lions. In this research, we proposed a new model of triadic prey-prey-predator. The new model was constructed using the new fractional differentiation based on the generalized Mittag-Leffler function due to the non-locality of the dynamical system of the three species. We presented the existence of a positive set of the solutions for the new model. The uniqueness of the positive set of the solutions was presented in detail. The new model was solved numerically using the Crank-Nicolson numerical scheme.

show abstract

Section: Introductionmentioning

confidence: 99%

A new nonlinear triadic model of predator–prey based on derivative with non-local and non-singular kernel

Alkahtani

Atangana

Koca

2016

Advances in Mechanical Engineering

View full text Add to dashboard Cite

show abstract

“…Our results may extend beyond informing studies of brain and biology. As introduced above with computerized load balancing and sharing, network connectivity maintenance, predator-prey networks, and economics (Lotka, 1910 ; Goel et al, 1971 ; Gandolfo, 2008 ; Wan et al, 2008 ; Allan et al, 2010 ; Shtessel et al, 2012 ; Arpaci-Dusseau and Arpaci-Dusseau, 2015 ), we assert that resource-utilization generally, causes the emergence of oscillations and periodic components. Here, we illustrate an analogous relationship, with oscillatory dynamics and energy requirements in the brain.…”

Section: Discussionmentioning

confidence: 63%

“…Models of resource or energy usage and constraint in other networked systems may also provide insight into modeling neuroenergetics. Lotka-Volterra equations have also been used in economics for many years to model resource interactions between industries and sectors (Gandolfo, 2008 ), which may produce oscillatory interactions as well. Within graph theory, related questions include how to maximize graph connectivity with limited or unreliable functional links between nodes (Wan et al, 2008 ), a task which the brain may perform.…”

Section: Introductionmentioning

confidence: 99%

Energetic Constraints Produce Self-sustained Oscillatory Dynamics in Neuronal Networks

et al. 2017

View full text Add to dashboard Cite

Overview: We model energy constraints in a network of spiking neurons, while exploring general questions of resource limitation on network function abstractly.Background: Metabolic states like dietary ketosis or hypoglycemia have a large impact on brain function and disease outcomes. Glia provide metabolic support for neurons, among other functions. Yet, in computational models of glia-neuron cooperation, there have been no previous attempts to explore the effects of direct realistic energy costs on network activity in spiking neurons. Currently, biologically realistic spiking neural networks assume that membrane potential is the main driving factor for neural spiking, and do not take into consideration energetic costs.Methods: We define local energy pools to constrain a neuron model, termed Spiking Neuron Energy Pool (SNEP), which explicitly incorporates energy limitations. Each neuron requires energy to spike, and resources in the pool regenerate over time. Our simulation displays an easy-to-use GUI, which can be run locally in a web browser, and is freely available.Results: Energy dependence drastically changes behavior of these neural networks, causing emergent oscillations similar to those in networks of biological neurons. We analyze the system via Lotka-Volterra equations, producing several observations: (1) energy can drive self-sustained oscillations, (2) the energetic cost of spiking modulates the degree and type of oscillations, (3) harmonics emerge with frequencies determined by energy parameters, and (4) varying energetic costs have non-linear effects on energy consumption and firing rates.Conclusions: Models of neuron function which attempt biological realism may benefit from including energy constraints. Further, we assert that observed oscillatory effects of energy limitations exist in networks of many kinds, and that these findings generalize to abstract graphs and technological applications.

show abstract

“…The population dynamics models have mature mathematical foundations and successful applications in a diverse set of practical problems even outside of biology (Neal, 2004 ; Singh and Uyenoyama, 2004 ). For example, Gandolfo ( 2008 ) applied the predator-prey equations in economics to model resource interactions between industries. Neural network activity has been also modeled (Moreau et al, 1999 ; Burroni et al, 2017 ) by population ecology equations to describe the natural oscillations in neuronal networks.…”

Section: Resultsmentioning

confidence: 99%

Population Dynamics and Long-Term Trajectory of Dendritic Spines

Özcan

Ozcan

2018

Front. Synaptic Neurosci.

View full text Add to dashboard Cite

Structural plasticity, characterized by the formation and elimination of synapses, plays a big role in learning and long-term memory formation in the brain. The majority of the synapses in the neocortex occur between the axonal boutons and dendritic spines. Therefore, understanding the dynamics of the dendritic spine growth and elimination can provide key insights to the mechanisms of structural plasticity. In addition to learning and memory formation, the connectivity of neural networks affects cognition, perception, and behavior. Unsurprisingly, psychiatric and neurological disorders such as schizophrenia and autism are accompanied by pathological alterations in spine morphology and synapse numbers. Hence, it is vital to develop a model to understand the mechanisms governing dendritic spine dynamics throughout the lifetime. Here, we applied the density dependent Ricker population model to investigate the feasibility of ecological population concepts and mathematical foundations in spine dynamics. The model includes “immigration,” which is based on the filopodia type transient spines, and we show how this effect can potentially stabilize the spine population theoretically. For the long-term dynamics we employed a time dependent carrying capacity based on the brain's metabolic energy allocation. The results show that the mathematical model can explain the spine density fluctuations in the short-term and also account for the long term trends in the developing brain during synaptogenesis and pruning.

show abstract

Giuseppe Palomba and the Lotka-Volterra equations

Cited by 48 publications

References 7 publications

A new nonlinear triadic model of predator–prey based on derivative with non-local and non-singular kernel

A new nonlinear triadic model of predator–prey based on derivative with non-local and non-singular kernel

Energetic Constraints Produce Self-sustained Oscillatory Dynamics in Neuronal Networks

Population Dynamics and Long-Term Trajectory of Dendritic Spines

Contact Info

Product

Resources

About