Stability and electronic circuit implementation of Lotka–Volterra model with delay

ABSTRACT

In this work, we study a Lotka–Volterra system with delay. We carry out an analytical study from which there emerge three equilibrium points. In the absence of delay, two of these points are unstable whatever the choice of the parameters of the system, and the other one is stable according to the chosen parameters. With delay, and looking only at the point of positive coexistence, we find that it can cause not only instability, oscillations and switching stabilities, but also chaos. In addition, the analytical study revealed the phenomenon of switch stability, thus increasing the zones of instability. Time traces, phase portraits and bifurcation diagram obtained by numerical simulations complement the analytical investigations. Finally, we propose an electronic circuit with delay whose simulation presents the different phenomena observed numerically, thus validating this new electronic circuit with complex dynamics.

KEYWORDS:

• Lotka–Volterra model
• delay
• bifurcation
• chaos
• electronic circuit
• stability
• filters

Disclosure statement

No potential conflict of interest was reported by the authors.