Abstract
The well-known Fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified model is analyzed both analytically and numerically. A comparatively new technique residual power series method is used for finding approximate solutions of the modified Fisher model. A new technique combining Sinc-collocation and finite difference method is used for numerical study. The abundance of the bird species Phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters. We conjecture non-diffusive and diffusive fractional Fisher equation represents the same dynamics in the interval (memory index, α∈(0.8384,0.9986)). We also observe that when the value of memory index is close to zero, the solutions bifurcate and produce a wave-like pattern. We conclude that the survivability of the species increases for long range memory index. These findings are similar to Fisher observation and act in a similar fashion that advantageous genes do.
Original language | English |
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Pages (from-to) | 81-93 |
Number of pages | 13 |
Journal | Physica A: Statistical Mechanics and its Applications |
Volume | 438 |
DOIs | |
Publication status | Published - Jul 17 2015 |
Externally published | Yes |
Keywords
- Approximate solutions
- Fisher's equation
- Fractional differential equation
- Generalized Taylor series
- Residual power series
- Sinc method
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics