Dynamically consistent discrete Lotka–Volterra competition systems

Abstract

Consider the difference equation competition system

where , , , , and for all . This 2D map is derived using a non-standard finite difference method from the continuous time Lotka–Volterra competition system

Then under the condition that and , the dynamics of the discrete system is almost the same as the continuous system. The difference equations are dynamically consistent with their continuous counterparts. The positivity of solutions, monotonicity of solutions and stability conditions of equilibria are all preserved.

Keywords:

• Lotka–Volterra
• dynamically consistent
• monotonicity
• non-standard finite difference method

Acknowledgement

The authors would like to thank the reviewers for their helpful comments and suggestions.

Notes

1. [email protected]

Additional information

Notes on contributors

Glenn Lahodny

1