# Lotka-Volterra Population Biology Models with Negative Feedback and their Ecological Monitoring

@inproceedings{Vaidyanathan2015LotkaVolterraPB, title={Lotka-Volterra Population Biology Models with Negative Feedback and their Ecological Monitoring}, author={Sundarapandian Vaidyanathan}, year={2015} }

Lotka-Volterra population biology models are important models that describe the interaction between various biological species considered as predator-prey system. This work describes a Lotka-Volterra population biology model with negative feedback. We show that for this biological model, the predator and prey species have stable coexistence. Then we shall propose ecological monitoring of the population biology model by constructing a nonlinear exponential observer for the population biology…

No Paper Link Available

## 80 Citations

### Global Chaos Synchronization of the Lotka-Volterra Biological Systems with Four Competitive Species via Active Control

- Mathematics
- 2015

Chaos is an important applied area in nonlinear dynamical systems and it is applicable to many real-world systems including the biological systems. In the biological systems, there is great interest…

### Active Control Design for the Anti-Synchronization of Lotka- Volterra Biological Systems with Four Competitive Species

- Mathematics
- 2015

Chaos is an important applied area in nonlinear dynamical systems and it is applicable to many real-world systems including the biological systems. In the biological systems, there is great interest…

### Dynamical analysis, stability and discretization of fractional-order predator-prey model with negative feedback on two species

- Mathematics
- 2021

The Lotka-Volterra model is an important model being employed in biological phenomena to investigate the nonlinear interaction among existing species. In this work, we first consider an integer…

### Hybrid Synchronization of the Generalized Lotka-Volterra Three-Species Biological Systems via Adaptive Control

- Mathematics
- 2016

The phase portraits of the 3-D generalized Lotka-Volttera system when the system undergoes chaotic behaviour are depicted and adaptive biological control law for achieving global and exponential hybrid chaos synchronization of the states of the generalized Lotko-Volterra three-species biological systems with unknown parameters is derived.

### Global Chaos Control of the Generalized Lotka-Volterra Three-Species System via Integral Sliding Mode Control

- Mathematics
- 2016

Since the recent research has shown the importance of biological control in many biological systems appearing in nature, this research paper investigates research in the dynamic and chaotic analysis…

### Fixation in the stochastic Lotka-Volterra model with small fitness trade-offs

- MathematicsJournal of Mathematical Biology
- 2022

We study the probability of fixation in a stochastic two-species competition model. By identifying a naturally occurring fast timescale, we derive an approximation to the associated backward…

### Explicit probability of fixation formula for mutual competitors in a stochastic population model under competitive trade-offs

- Mathematics
- 2020

An approximation to the BKE is derived that exploits both the small fitness differences and a fast timescale within the dynamics and allows for analytically finding an explicit formula for the probability of fixation.

### Global Chaos Control of the FitzHugh-Nagumo Chaotic Neuron Model via Integral Sliding Mode Control

- Biology
- 2016

The qualitative properties of the well-known FitzHugh-Nagumo (FHN) chaotic neuron model, which is a two-dimensional simplification of the Hodgkin-Huxley model of spike generation in squid giant axons, are investigated.

### Anti-Synchronization of Enzymes-Substrates Biological Systems via Adaptive Backstepping Control

- Engineering
- 2016

In the recent decades, there is significant interest in the literature in the application of chaos in physical, electrical, chemical and biological systems. This paper investigates research in the…

### Adaptive Integral Sliding Mode Control of a Chemical Chaotic Reactor System

- PhysicsApplications of Sliding Mode Control
- 2017

It is shown that the chemical chaotic reactor system has three unstable equilibrium points and a stable equilibrium point and the main adaptive control and synchronization results are established using Lyapunov stability theory.

## References

SHOWING 1-10 OF 26 REFERENCES

### Nonlinear Systems

- Mathematics
- 2013

Nonlinearity is ubiquitous in physical phenomena. Fluid and plasma mechanics, gas dynamics, elasticity, relativity, chemical reactions, combustion, ecology, biomechanics, and many, many other…

### New results on general observers for discrete-time nonlinear systems

- MathematicsAppl. Math. Lett.
- 2004

### New results and examples on observer designof nonlinear systems around equilibria

- MathematicsMath. Comput. Model.
- 2004

### Exponential observer design for discrete-time nonlinear systems with real parametric uncertainty

- Mathematics
- 2003